ÖAsk Dr. Risk! TM Columns
from 1998
Other columns: current 1999
1998 1997 1996
Five Questions (11/28/98)
Questions 1-3: Dear Dr. Risk – Three questions:
1. Why do we engineer financial products? Is this a passing
fad? Why or why not?
2. How do you use options and futures together to hedge interest
rate risk, commodity price risk, and foreign currency risk?
3. Using the put-call parity, can we tell whether put option
prices depend on the same factors as in call option?
Thank you – Paula
Answer: Dear Paula – Thanks for some fun questions.
1. We engineer financial products for the same reason that we engineer cars and stereos – because product design is too important to leave to chance. Of course, it is also too important to leave to engineers. That's why we involve customers, salespersons, traders, and lawyers in the process.
Financial engineering is not a passing fad, because the engineered products provide new and/or less expensive ways to fill important needs that customers perceive, such as avoiding taxes and regulations, sidestepping accounting rules, reducing transactions costs, expressing market views, and completing markets. Note: You or I may not agree that such uses of financial engineering are "socially" useful, but the customers seem to believe that they are, and that matters, a great deal.
2.a. First, a philosophical point that may have practical significance. I believe that "my" ("your") portfolio is much too narrow a focus for me (you). Each of us is on the earth but a short time, but one’s genes may survive with positive probability, perhaps into eternity. Many of us expect to inherit more than chromosomes from our parents and most of us want to bequeath more than chromosomes to our offspring. Thus, I think that one should adopt a "family" point of view that includes the investments of one’s parents, spouse, siblings, and children – i.e., all those who share one’s genes.
Second, PERSONALLY, I don’t use options and/or futures to hedge risks, because I believe that the transactions costs for me are too large for little old, retail customer me, relative to the uncertain gains in utility. I believe that I am a fairly ordinary investor, with ordinary beliefs and an average utility function, so I want an ordinary portfolio – the market portfolio.
Third, one might achieve an approximation of the market portfolio by investing in a specific portfolio with a certain amount of diversification, limited by transactions costs and capital gains taxes. Another way to achieve diversification at low cost is to invest in one or another of the Vanguard index funds.
2. b. ONE can use futures to create or hedge price and currency exposure, and options to hedge price and volatility exposure. The principals are roughly the same for any sort of underlying risk. The details are different and important. I’ll paint only the broad outline for the case of interest rate risk.
Suppose that you have dollar and DEM swaps and swaptions. First, eliminate exposure to volatility of forward rates. Second, eliminate exposure to levels of forward rates. Third, eliminate exposure to foreign currencies.
Step #1. You can build a theory of swaption volatility that depends on the volatility of the underlying forward rates and the pairwise correlations. Based on that, you can find the portfolio of Euro futures options that hedges your swaption volatility risk, leaving you with correlation risk, some interest rate risk in two currencies, and currency exposure. Of course, the effectiveness of your hedge depends on the quality of your theory. You're probably stuck with the correlation risk, unless you do some OTC spread or average trades. Also, remember, when disaster strikes, all correlations will approach unity and a disaster of a magnitude that you probably didn't anticipate could happen. Hedge the remaining interest rate risk as with the swap risk in step #2. Hedge the remaining currency exposure as in step #3.
Step #2. If you have a portfolio of dollar (DEM) swaps and residual interest rate risk from the swaptions, you can form a replicating portfolio of cash dollars (marks) and Eurodollar (Euromark) futures contracts. Hedge your interest rate risk by shorting the Euro contracts in the replicating portfolio. Of course, this assumes that the contracts are liquid and that basis risk between swaps and futures is nil. That leaves currency exposure, which you hedge as in step #3.
Step #3. You have hedged all volatility risk and interest rate risk and have a portfolio that is equivalent to a number of cash dollars and cash DEM. Hedge the currency risk with the nearby currency futures contract. Of course, the nearby isn’t the cash currency, so you have some basis risk. Hedging in the cash market might make more sense.
3. Put-call parity is useful, where it applies, but it doesn’t always tell you that put option prices depend on the same factors as call options. Consider two cases:
American options – put-call parity doesn’t hold, because you might have early exercise of calls and puts under different conditions. For example, if the dividend yield is positive and the interest rate is zero, you may have early exercise of the calls, but never early exercise of the puts. If the dividend yield is zero and the interest rate is positive, you may have early exercise of the puts, but never early exercise of the calls.
European, deep in-the-money calls on a foreign currency and corresponding deep out-of-the-money puts. These calls are roughly equivalent to forward contracts, hence sensitive to the underlying exchange rate, the foreign rate of interest, and the domestic rate of interest. The corresponding puts are deeply out of the money, hence worthless and insensitive to all these things.
Sound reasonable? – Dr. Risk
Questions 4-5: Dear Dr. Risk – More questions:
4. What are the uses of swaps?
5. And how can I illustrate the cases with graphs and numerical
examples?
Thank you – Paula
Answers 4-5: Dear Paula – You're wearing me out.
4. Whenever you enter a contract, in which you mimic the return of going long one investment and short another, without a cash outlay or receipt, you are doing a swap. The uses of swaps are infinite. The principal uses are speculation and hedging (or risk management). For example, one might want to put on a spread trade to express a directional view in two risk factors. Swaps may also be good for obtaining high leverage, without appearing to naive on-lookers as if you are doing so. However, these days many swaps require collateral, which suggests that they aren't as potent a way to lever, as before.
5. Wish I could take the time to help you more here. I'll just say that I have found the Excel or Lotus 1-2-3 spreadsheet an excellent vehicle for illustrating cash flows from swaps. – Dr. Risk
Talking Turkey (11/28/98)
Question: Dear Dr. Risk – Hello... I want to learn more about swaps(currency and interest rate),how can we use this kind of derivatives(in which conditions), are they used widely in the world and Turkey( if you Know)? Thank you very much. – Oyku
Answer: Dear Oyku – Thanks for asking about such Turkish delights as Turkish lira swaps. Fortunately, the principals of swaps are global, timeless, and fairly standard material for textbooks, handbooks, and other references. You might want to search Amazon.com for books about swaps.
People use swaps everywhere that it allows them to lower transaction costs and stay one step ahead of the regulators, tax men, accounts, etc., so I tend to think that they use them in Turkey. Unfortunately, Dr. Risk knows nothing about the specifics of financial regulation, tax law, or accounting standards on either bank of the Bosphorus and is much more conversant in topics about which you no doubt care little or nothing, such as the practice of nepotism among the grand mullas – such as the Sheik ul Islam or Anatolian or Rumelian Kadiaskars of the Ottoman Empire. But, I digress. A possible source of specifically Turkish information is the Global Finance Association's meeting in Istanbul, Turkey, April 7-9, 1999. Its web site contains much more information. Good luck! – Dr. Risk
Asian Options (11/28/98)
Question: Dear Dr. Risk – I am trying to understand more abour Asian, or Interest Rate options. If you could tell me a little about their development, types and pricing issues, I would be extremely grateful. – Darren
Answer: Dear Darren – Thanks for asking about Asian options.
An Asian option has an underlying that is an average over time of a particular price or interest rate. An average price option has an underlying average over time of the observed values of a share or commodity price. An average rate option is like an average price option, except that the underlying is an interest rate or exchange rate. The Asian option can be European or American. The American options are much more difficult to price.
My guess is that the term has no descriptive significance, and is just an historical accident. I believe that Bankers Trust's Tokyo office did the first Asian options circa 1988. They were in Asia. They were doing options that weren't standard American or European options, so they called the options Asian options.
When my BT colleagues in New York first described the Asian product to me, I did not understand at first that the underlying was the average. I thought that the strike was the average. For a couple of days we mystified each other in our emails, until finally I realized that we were writing about different things. An average strike option has a strike price that is the same average over time as the underlying in the average price option or average rate option. Some people include average strike options as a variety of Asian option.
Personally, I prefer the more precise terms average price option, average rate option, and average strike option to the less descriptive, generic term, average option, which I pefer to the even more cryptic "Asian option".
The Asian option's underlying average is typically arithmetic, but some average options use different averages, including geometric, harmonic, and more general averages. Indeed, the minimum or maximum along a path is a weighted average of the values along the path, with all the weight going to the minimum or maximum value. The harmonic average of the Xi is the reciprocal of the arithmetic average of the reciprocals of the Xi. The relationship of the averages of the Xi is
minimum £ harmonic average £ geometric average £ arithmetic average £ maximum.
Check on relationship of averages of {1, 2}: 1 £ 1/ (3/4) £
Sqrt(2) £ 3/2 £ 2.
The three main ways for pricing average options are: (a) Monte Carlo simulation, (b) analytic approximation, and (c) finite difference.
The Monte Carlo approach involves simulating a path for the underlying price or rate, computing the appropriate average along that path, computing the payoff for that average, taking the arithmetic average of the payoffs over all paths in the sample, and discounting as appropriate.
The analytic approximation involves substituting appropriate forward price and volatility into Black's model. The forward price of the average is the average of the corresponding forward prices. The volatility is a more complicated expression, which is approximately the volatility of the underlying price, divided by the square root of three. Levy was a pioneer of this approach.
Wilmott, Dewynne, and Howison (1993 book) describe the finite difference approach.
I'm going to skip the part about interest rate options. That's a broad subject on which many people have written extensively, and that writing is readily accessible.
Even just the topic of Asian options is broad, and this is all I can say at this time. Good textbooks, such as Hull's provide some discussion of the topic and more complete references than I gave. – Dr. Risk
Anatomy of a Trade (11/28/98)
Question: Dear Dr. Risk – I have a question, I hope you have an idea where I could get help:
I am writing a master's thesis on "Mechanical Trading Systems" and although I have the contract specifications of the different commodities / financials I have problems when calculating the Price Change in Ticks, Price Change in Points and the corresponding profit & loss and Return on Margin/Return on Account correctly. Above all I get confused when comparing metals with currencies, interest rates with grains, etc.
The following would be the best help:
I would need an illustration (e.g. Excel-spreadsheet, Text File, etc.) of the "life"/anatomy of different trades from Entry to Exit across the different commodities/financial futures, including (not necessarily all items):
Price, Price Change in Ticks, Price Change in Points, Entry-Price, Exit-Price, amount in dollars at risk, Number of Contracts, Margin required (initial + maintenance), corresponding Leverage Factor and corresponding Margin-Equity Ratio, Profit/Loss, Return on Margin, Return on Account, and Current Equity.
...That's a lot...
Any ideas how and where to obtain this information? - Do you maybe have something you can copy and paste out of an existing LOG-File, Excel-spreadsheet, etc., so that you can save time? Regards – Thomas
P.S. Austria/Europe --> high mountains --> Mozart --> no kangaroos
Answer: Dear Thomas – That sounds like a fascinating and extremely applied project. I imagine that you’ll learn a great deal in completing it. You need the sort of information that the exchanges should be prepared to supply, and I believe I have seen such information for every contract for which I have sought it. The exchanges want customers to make more trades, so they have to educate the customers about the motivation for trading to shift the demand curve for trading to the right, and about the details of trading to lower the cost of trading.
Try the following for each contract that interests you: Find a link from my "links" page (Links.html) to the relevant exchange’s site, and you may be able to request this information directly via the exchange’s web site. Otherwise, find the telephone number for information, and a call should do the trick. If you cannot find the relevant link, try to go through sites to which I provide links, such as Waldemar’s.
Good luck! – Dr. Risk
P.S. Thanks for the geography / history / biology lesson about Austria. I will stop my vain search for Austrian kangaroos and Australian Mozarts.
Vulnerable Options (9/28/98)
Question #1: Dear Dr. Risk – What is a "vulnerable option" ? Enquiring minds want to know. – Alyce
Question #2: Dear Dr. Risk – I have found a definition of a "vulnerable option in a paper:
- Emilio Barone, Giovanni Barone-Adesi, and Antonio Castagna, "Pricing bonds and bond options with default risk," European Financial Management (Vol 4, No 2, 1998, pp.231-282).
It appears this term is used to mean options written by a defaultable party on either risk-free or defaultable options. I guess "vulnerable" makes sense in this case, because there is credit risk not associated with the credit risk of the underlying asset. – Alyce
Answers to #1 and #2: Dear Alyce – Thanks for asking your question of general interest about "vulnerable option" and supplying me with an authoritative answer to your own question. That's the kind of participation we could use more of around here. Professor Barone was kind enough to send me a copy of the paper, which I recommend highly. The introduction contained a highly readable review of the literature and a highly technical discussion of many of the important issues.
The topic of "vulnerable derivatives" is extraordinarily important. Strictly speaking, all derivatives are "vulnerable", because you can never be sure that your counterparty will pay you what he owes. The degree of "vulnerability" depends on the collateral backing up the counterparty's obligation to pay. This collateral can be of a general nature, including all the assets that creditors could go after in bankruptcy. The collateral can be more specific, such as all the contracts included in a bilateral netting agreement, the collateral backing a clearing house's guarantee of futures or futures options contracts, or the collateral for a specific deal.
As a practical matter, most derivatives are vulnerable. Today, even though specific collateral backs many swaps, it does not back all, and default is a constant threat of unknown dimensions for such deals. Standard pricing models don't begin to deal with this issue adequately. As Barone et al. write, more recent researchers have approached defaultable claims in two main ways: (1) the "structural", "firm value" approach, and (2) the "reduced-form", "hazard rate" approach.
The structural approach appears to me to convert a derivative product with an n-dimentional promised payoff into a derivative with an actual (n+m)-dimensional payoff, m³ 0. For example, a zero coupon bond is a promise to pay that may appear to have zero dimensions of risk, but actually has one, as Black-Scholes (1973) clearly explained. Implementing this approach can be difficult, because the number of risk factors can be large and sorting out the actual payoff function can be difficult, as when one needs to know the entire capital structure of a firm, in order to figure out the payoffs for senior and junior, subordinated debt. The approach may no be precise, if political or other complex considerations, in addition to the issues of positive net worth, influence the default decision.
The reduced form approach makes all the necessary assumptions to bypass the obvious complications of the structural approach. This might involve modeling default as a Poisson process, and the recovery rate as either given, time dependent, or stochastic.Advocates of this approach like the way it finesses the tough issues of the structural approach. However, one faces the problem of making sure that the assumptions are not arbitrary and misleading.
For a better theoretical understanding of the relevant issues and ways to deal with them, see the article by Barone, Barone-Adesi, and Castagna. I found an additional, textbook discussion of pricing and hedging vulnerable derivatives in Jarrow, Robert, and Turnbull, Stuart, Derivative Securities, Cincinatti, South-Western, 1996, pp. 574 et seq.
For what it's worth, I prefer the adjective "defaultable" to "vulnerable", because it is more specific. I lean toward the structural approach, because the reduced form approach seems too subjective. Thanks, also, to Ingo Schneider for counsel about vulnerable options that goes beyond what I have mentioned here.
– Dr. Risk
Planting Perfect Hedges on Real Estate [Loans] (9/28/98)
Question: Dear Dr. Risk – I work for a real estate developer that has floating rate debt set monthly at the 30 day LIBOR. The debt has a five year term. I am interested to know the benefits and detriments of the various derivative products that can cap or lock in a rate across these 60 periods. Thanks – Don
Answer: Dear Don – Interesting issue. I have a fondness for applying derivatives to real estate and real estate finance, but don't have many opportunities.
Initially, I'll assume that the loan doesn't amortize, although things don't change much with amortization. You have 60 floating payments, proportional to LIBOR and to the face amount of the loan. You want to eliminate the variability in your cash flows over the next five years. Your two main ways of doing this are with a swap or with a cap. A collar is possible.
- Swap: You could swap any one of those into a fixed payment with an FRA. You could swap all of those payments into fixed payments with a vanilla interest rate swap at zero up front cost. The advantage is that you know exactly what you'll have to pay, and you win if interest rates rise. The downside is losing if interest rates fall.
- Cap: You could buy a cap struck at (say) 7%. Then, if your floating payment goes above 7%, your cap indemnifies you. Your payment still floats, but has a ceiling at 7%. This protects you against a rise in rates, but has an up front cost.
- Collar: You could enter into a collar, buying the cap and paying for it by selling a floor of equal value. This has no up front cost. It protects you on the upside, but you give up the benefit on the downside of rates. Excessive transactions costs make this not so desirable to the customer, although the dealer may love it.
If your loan amortizes, you could have an amortizing FRA, swap, cap, or collar. Conceptually, the amortizing products are easy to understand in terms of corresponding, non amortizing products. For example, a two-year loan, $100 loan that amortizes 50% at the end of one year is like (a) a non amortizing, two-year, $50 loan, plus (b) a non amortizing, one-year, $50 loan. You would hedge the amortizing loan with the sum of the hedges for the non amortizing loans.
I've got a question for you: How are you sure that LIBOR is the right floating rate for this loan? That would suggest the same amount of risk as with interbank loans. Is the spread off LIBOR equal to zero?
A question for anybody: It's interesting to me that some people want to swap floating payments for fixed to eliminate uncertainty, while others want to swap fixed payments for floating for the same reason. Floating payments involve uncertain cash flows, but relatively certain present value. Fixed payments are certain, but with uncertain value. What are the differences in preferences (e.g., utility functions) that lead to this difference in the preferred cash flow streams?
This is just what pops into my head. Feel free to ask a follow up question.– Dr. Risk
P.S. Maybe you can bring my real estate finance education up to date a bit. I would have thought that a five-year loan for a developer would be rare. I guess it's not construction financing for a single building. Could it be for a housing development that you are selling over a period of at least five years?
Add-in Reviews (9/28/98)
Question: Dear Dr. Risk – We were looking at excel based analytics for pricing dreivative products. Where can we see your review of the available software ? – Mike
Answer: Dear Mike – Derivatives Strategy, August 1998, contains the "Spreadsheet Shootout". I think you can subscribe via http://www.derivatives.com. – Dr. Risk
Try Trojans for Cheap Protection (9/28/98)
Question: Dear Dr. Risk – Suppose you have a stock which currently sells for $20 and you are concerned that the price could fall to $15. Furthur suppose that buying a put at $15 this level is too expensive for your liking and that funding this at zero cost by selling a call at $25 is undesirable because you have a view that if the stock goes above $25 then it is extremely unlikely to ever go down to $15. What kind of option or dynamic option strategy do you think would be most appropriate for this situation? Cheers, – Tommy Tucker
Answer: Dear Dear Mr. Tucker – Thanks for the question about buying cheap downside protection.
Your mention of knockout options raises the important issue of path dependent derivatives, which allow you to buy a payoff that depends on all the values that a price takes along its path from inception to expiration, not just on the terminal price. Specifically, you said that you didn't think that the price would rise from 20 to 25, then fall below 15. An up-and-out put option, struck at 15, with an outstrike or barrier of 25 would give you the protection you wanted. (Which is just restating what you said.) The U&O put will be cheaper than an ordinary put. However, I shouldn't think it would be much cheaper, given reasonable volatilities and investment horizons, because the probability of the paths you give up is small.
Unfortunately, generally speaking, I don't believe that the market overprices or underprices any derivatives significantly, and that includes the one in the previous paragraph. Cheap downside protection is like a cheap sweater – it's likely to fall apart when you most need it. In active markets you get what you pay for. Consequently, I don't have any suggestions about what path-dependent derivative to buy for "cheap" protection.
If you decide that a particular derivative offers what you want, and nothing more, then you should shop around for the best price. Don't assume that a dealer with which you have a long "relationship" is sure to give you the best price. Find out for sure. An exchange-traded derivative is likely to be cheaper than any OTC derivative.
Due to sizable transactions costs, I would doubt that a dynamic strategy will be best, unless you had a strong view that the path would be smooth and transactions costs would be as small as possible.
If you close out your "zero cost collar" when the underlying price approaches 25, then you will be paying out the price of the previously OTM call to buy it back, and you will be giving up your downside protection. Given the view that you had stated in your previous message, you may see this as a reasonable action.
When I started working for an equity derivatives dealer, I thought that customers would come to me with ideas that I would whip into shape, turn into derivatives, and price. Turns out, the main idea the customers had was that they wanted to "make money" – in the sense of beating the market – had no idea how to do it, and wanted me to tell them. At that I never had any success. Nor did I ever make a serious effort. My experience is relevant here, because you asking me to identify underpriced derivatives, and I doubt that they are available, because (a) the market rules and (b) transactions costs tend to eat active traders alive.
Good luck.– Dr. Risk
Pulp Fiction? (9/28/98)
Question #1: Dear Dr. Risk – i work for a large corporation that spends a significant amount purchasing paper, yet cannot pass paper price increases on to customers. given the volatility in pulp and paper prices -- what risk management strategy would you recommend? – Frantic
Answer #1: Dear Frantic – From your e-mail address, it would appear that you work for a large consulting firm. I realize that the firm must buy a lot of paper, with all that printing and copying of reports, but find it hard to imagine that managing the risk of fluctuations in pulp and paper prices is worth a lot of thinking. Also, I find it hard to understand why you cannot pass the rise in paper prices along to customers.
Please send enough details about the problem – whether your consulting firm has it or a client does – so I can give a useful answer. – Dr. Risk
Question #2: Dear Dr. Risk – the question was asked on behalf of a client -- i cannot reveal the name of the company, however . . . they use the paper for [what they publish.] . . . they are currently purchasing [a big] percent % of North American output of one particular grade … what else do you need to know? – Frantic
Answer #2: Dear Frantic – Getting information from you is a little like getting the truth, the whole truth, and nothing but the truth from President Clinton – but much easier. Since the government hasn’t given me $40 million to spend to dig up your facts and report to Congress, I’m afraid that I must withdraw from this case. However, first, I’ll make a preliminary report.
First, and important to me, thanks for asking a question that requires thinking like an economist, not just acting like an applied mathematician or engineer – not that there's anything wrong with that. Based on what you’ve told me – which, I hasten to add, isn’t much – your client doesn’t have a risk management problem. He has a business economics problem.
You said that you’ve got a client – a publisher and a corporation – that is unhappy that it "cannot pass paper price increases on to customers" and wants to know how to pass on 100% of said increased costs. No firm ever passes on 100% of an increase in the cost of a major input to an entire industry. The reason is simple – the industry demand curve’s slope is negative. If the supply curve shifts up by x, equilibrium requires a move up the demand curve and down the new supply curve. The new equilibrium is at a higher price – but not x higher – and a lower quantity.
By the way, I infer from your remarks that your client is both a monopsonist and a monopolist in its market. (That is, your client has monopoly and monopsony power, which means it is a "big" buyer and seller.) Your client is apparently a monopsonist, because it buys such a large percentage of that sort of paper. It’s a monopolist, because firm – and industry – output in publishing is roughly proportional to the quantity of paper that it buys. This doesn’t change the basic answer, but adds details.
You might want to draw a picture to see the following. Under ordinary circumstances, a rational monopolist never passes along 100% of the shift in his marginal costs for reasons that go beyond the above discussion of increased costs for an industry. The monopolist's marginal revenue curve lies below and is steeper than his average revenue (demand) curve. The monopolist produces where marginal revenue equals marginal cost. When the marginal cost curve shifts up by x, production falls. Marginal revenue rises by as much as marginal cost, but by less than x, because the marginal revenue curve is not vertical. Price on the demand curve rises even less than marginal revenue does, because the demand curve isn’t as steep as the marginal revenue curve. Consequently, the change in market price is less than the shift up in the marginal cost curve, and production and profit decline.
That gives me an idea for a new division of The William Margrabe Group, Inc. – the monopoly management practice. One product would be therapy for monopolists who don’t understand why they behave the way they do, and feel bad about every penny that gets away from them. The publishing group would sell my book, Producers who charge too much – and the consumers who pay the price. – Dr. Risk
Spam! Spam! Spam! Spam! II (8/28/98)
Question: To: DoctorRisk@aol.com – Subj: RE: MAJOR BUY ADVISORY!-- M K I I
The top-rated Wall Street based P. J. Morgan Newsletter has initiated a "strong buy" recommendation on:
Mark I Industries, Inc.
M K I I
1/2 ($.50/share)
THEY ARE PROJECTING A $4.00 SHARE PRICE SHORT-TERM (BY THE END OF THIS YEAR)!
M K I I is a featured buy based on a thorough technical and fundamenral analysis of the company. Earnings are estimated to go from $.05/share in fiscal ‘98 to $.23/share in 1999. Furthermore, a large short position in the stock needs to be covered (bought) which will only increase the upward momentum.
P. J. Morgan has M K I I rated a strong immediate BUY as well as a long-term hold position.
For further information on M K I I go to:http://quote.yahoo.com/ – advisor83098@best.com
Answer: Dear advisor83098 – Thanks for sending me three separate messages, any one of which would have been a perfect example of spam hyping a stock. Please excuse me for answering your message with a lot of questions:
- Is the P. J. Morgan Newsletter related to JP Morgan, the commercial bank? Does such a newsletter exist, or did you just make it up?
- What am I supposed to make of your message that seems to say that the stock trades at 1/2, when that's the asking price and the last trade was at 3/8 – the bottom of the "52-week Range" – according to http://quote.yahoo.com/q?s=MKII&d=2b.
- Do you really expect me to give credence to this newsletter that I've never heard of and its $4/share projection for this stock by the end of 1998, when people who have followed this stock and have money at stake are pricing it at 3/8?
- What kind of idiot do you take me for?
- What kind of idiot sees a buy signal in this sort of message?
– Dr. Risk
Equity Derivative Resources (7/28/98)
Question: Dear Dr. Risk – I was wondering if you could point me to the right direction where I can find information on Equity Derivatives (Equity Swap, Options, Warrants, CB's, etc etc) for Asian Market especially. Thank you in advance for your assistance. Sincerely – Kiki L.
Answer: Dear Kiki – Thanks for asking Dr. Risk about equity derivatives. However, I'm a bit puzzled. Your E-mail appears to originate from a major derivatives deal which has an active equity derivatives department. I realize some people left to go to a competitor, but I believe many stayed behind. So, I believe your firm has a vast amount of documentation on the subject, as well as many qualified persons. I refer you to some people I know there for more information. Also, your syndicate department is a pioneer in and major underwriter of derivative securities. They have much literature, too.
I would suggest the book, Equity Derivatives; Applications in Risk Management and Investment, London, Risk Publications, 1997. I'm a contributor to it, but would recommend it even if my chapter weren't there. It's out in hardback and paper. I didn't find it at Amazon.com. If you're a potential customer for equity derivatives, you might ask Murali Ramaswami at Lehman Brothers how you can get a copy. Otherwise, try to get it through Risk magazine.
The Handbook of Equity Derivatives, edited by Jack Clark Francis, William W. Toy, and J. Gregg Whittaker, is a classic, that is unfortunately now out of print. You may find it in a bookstore, such as the McGraw-Hill Bookstore, if you work in New York.
A number of other volumes about equity derivatives are available at Amazon.com, including:
- Equity
Derivatives Handbook by John Watson (Editor).
Amazon Price: $245.00 [On the expensive side, and I haven't seen it! – Dr. Risk].
Hardcover - 200 pages (1993)
Euromoney Publications PLC - Equity
Swaps : A Self-Study Guide to Mastering and Applying
Equity Swaps (Probus Professional Workbook Series on
Derivatives) by Coopers, Lybrand
Amazon Price: $55.00 [A bit elementary, but a real teaching tool. – Dr. Risk]
Your firm surely belongs to ISDA. They have abundant information about trading volume for OTC products. You have to figure out who is the right person to contact at your firm, so you can see that sort of information. – Dr. Risk
Compounding the Problem (8/28/98)
Question: Dear Dr. Risk – I want to price compound options with a Monte Carlo method. How and where can I find informations on the subject? – J-J
Answer: Dear J-J – If you want to price compound options on commodities, currencies, and equities, then methods that are faster and more accurate than Monte Carlo methods have been available for close to two decades, beginning with Robert Geske, "The Valuation of Compound Options," Journal of Financial Economics 7 (1979), pp. 63-81.
Of course, there are other sorts of compound derivatives, including installment options – e.g., a call on a call on a call … on a call – and compound options that depend on a stochastic yield curve. Monte Carlo methods might be the way to go for these. Also, building at least two models to price anything has its advantages.
If you’re convinced that you
want to use Monte Carlo methods, I'd say the way to go is to just
make sure you understand basic Monte Carlo pricing of options,
then tailor a model to suit your needs. Phelim Boyle started that
ball rolling with "Options: A Monte Carlo Approach," Journal
of Financial Economics 4 (1977), pp. 323-338. Alternatively,
any decent textbook about options or derivatives should introduce
you to Monte Carlo methods. An excellent book that covers Monte
Carlo and other numerical methods would be Press, et al., Numerical
Recipes in C;2nd ed. (New York:
Cambridge, 1992). For advanced ideas, you might try George S.
Fishman, Monte
Carlo (New York: Springer, 1996). I own both those books
and found them valuable. They are for sale at Amazon.com.
Have fun! – Dr. Risk
Heath, Jarrow, and Morton in Monte Carlo (8/28/98)
Question: Dear Dr. Risk – i found on your WEB Page a reference to Monte Carlo Implementation of the HJM model under the heading "Intermediate Derivatives Analysis". You mention there, that you offer a take away working spreadsheet for students. Im am interested in this spreadsheet and it would be nice if you can send it to me. I would also agree to pay a fee for this spreadsheet. Thank you very much in advance. – Gomer Taylor
Answer: Dear Gomer – Thanks for asking about the spreadsheet that contains the Monte Carlo implementation of the HJM model. Ordinarily, I distribute the spreadsheet only to clients who attend my presentation on the HJM model. When I make a presentation on the HJM model I include a workbook that has
- one sheet for input and output – inputs include a forward curve and a volatility grid
- one sheet of Monte Carlo pricing calculations
- one sheet of binomial pricing calculations
The Monte Carlo and binomial models have a single factor, which can be Gaussian, lognormal, or Cox-Ingersoll-Ross. An associated module contains Black's model in Visual Basic code.
The outputs include prices for the following products
- caplet/floorlet in advance/arrears on Libor^n
- 1-period and 4-period bond options
- swap
- swaption
using the following models
- Monte Carlo HJM
- binomial HJM
- and either an expedient, such as Black's model, or simple NPV pricing.
Thus, you can compare the results of three approaches to gain some confidence in each. The workbook is also useful as an explicit guide to coding the algorithm in a procedural language, such as Visual Basic, C or C++, JavaScript, or Java. I had a programmer code a C++ algorithm from this spreadsheet and my white paper on the subject.
May I suggest two ways to proceed:
- Perhaps your employer might put together an audience for one or more days of seminars, including one concerning the HJM model. Each attendee would receive a copy of the Excel workbook and my usual, extensive documentation.
- The workbook and white paper are for sale.
Please let me know if you and/or your employer want to explore either of these possibilities. – Dr. Risk
Real [Estate] Options (8/28/98)
Question: Dear Dr. Risk – I want to value an option to continue my office lease at the end of five years. I can use NAREIT's numbers as a proxy for volatility, what is the best method to value a one year, two year and five year option? How can I best find out about valuing real estate in a method other than NPV analysis? Thanks – Patrick
Answer: Dear Patrick – Thanks for some fascinating questions. I have long had an interest in real estate, as well as a more recent interest in options. I had a chance to combine the interests in one problem on only a few occasions.
I'm not certain I understand the contract that you want to price, but here's my guess: You have a lease for five years and pay monthly rent, in advance. After the term of the lease is over, continuing month-to-month at the going, floating rate is always an option.
You want to price a five year option on an n-year extension, where n = 1, 2, and 5. Thus, your contract sounds to me like an option on a swap with monthly fixed and floating payments. In general terms, I'd suggest thinking about this as you would think about pricing a swaption. Brokers commonly use Black's (1976) model on such swaptions. Alternatively, one could apply any of a large number of models to this problem, using the relevant equivalent martingale measure to take the expected value at the end of five years of the ratio of the value of the swap to the value of the balance in a money market account.
The common problem with pricing options on real estate equity, leases, and mortgage loans is that we can't ordinarily find the information we need to define the relevant risk neutral probability distribution, beginning with the form of the distribution and extending in the cases of normality and lognormality to volatility and forward rates. Since the three most important things about real estate are location, location, and location, each interest in real estate tends to be unique. Since each unique piece trades only infrequently, it is difficult to put together a historical series on a property. I spent a long time thinking about this problem when I wrote my dissertation on the value of farm real estate in the context of the Sharpe-Lintner asset pricing model. I ended up holding my nose and using USDA index numbers.
I'd like to hear more details about the method by which NAREIT collects its numbers, constructs what I guess is an index, what it purports to measure, and why you believe it is relevant for your problem. Of course, professional traders tend to avoid historical data, because the past – while prologue, as my father was fond of saying – does not always predict the future satisfactorily. Anyway, I'm glad you've solved the problem of volatility data, so I don't have to address it. How about the problem of forward rents?
Now, concerning learning about alternative methods of pricing real estate, besides NPV: Of course, modern portfolio theory and option pricing theory apply to real estate, just as well as to other assets – in principle. However, I don’t believe that practitioners use modern the
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