Exotic options [April 4] We ve looked at European and American Calls and Puts European options with general payoff functions From a theoretical point of view. This could be carried further, to more Exotic or Path Dependent options. For example Barrier options. Eg. European call with an upper knock-out barrier: The option payoff is (S T K 1 ) +, but only if S t K 2 for every t T. If the barrier is breached, the option is worthless. (Cheaper than a vanilla call, as the seller s risk is capped.) Asian options. Eg. Fixed strike Asian put: The option payoff is (K A) + where A = 1 a T a<k T S k is the average closing stock price over the a days ending at expiration. (Lowers volatility.)
Exchange Traded Options Contracts: Stocks [Apr 4] Exotics are always OTC. Pricing often takes implied volatility from exchange traded options and then plugs that into BSM to get a price for the exotic. Single Stock Calls & Puts CBOE sells American calls and puts on a selection of stocks (1 option = 100 shares) Montreal exchange sells the same, but for Canadian stocks. Index Calls & Puts CBOE sells European calls and puts on a variety of stock indices: S&P, Dow, Nasdaq, Russell; Other synthetic indices too eg the VIX (volatility index). Montreal exchange sells European calls and puts on the S&P TSX 60. Prices are quoted in index points, and settlement is $100 the positive part of the difference between the closing index value and the strike.
Options contracts on other assets [Apr 5] Currency Calls & Puts Eg. CME sells American calls & puts for exchanging $125,000 Euros for USD at a set exchange rate. Likewise other currencies. Montreal exchange sells European calls & puts for exchanging $10,000 USD for CAD. Can price using the same tree idea. Now what changes is the exchange rate, not a stock price. Usually model dynamics to be mean reverting rather than pure growth. Commodity Calls & Puts CBOT and CME sell calls & puts on U.S. commodities. Binomial tree now models the commodity price, but cost of carry enters into the calculation.
Options contracts on other assets [Apr 5] Options on Futures Calls & puts on futures contracts trade on many exchanges. Eg. stock index futures, currency futures, commodity futures, interest rate futures, etc. An advantage (eg for commodities) is that the option on a future will be settled in cash rather than in the underlying. Eg. Canadian Canola option is an option on Canola futures, traded on ICE Canada (Winnipeg). Binomial tree represents price moves in the underlying. Interest rate options Eg. options to buy/sell bonds, t-notes, etc. Eg. options to buy/sell bond futures, Eurodollar futures, etc. Tree models (mean reverting) changes in risk free int. rate.
Other OTC options contracts [Apr 5] Credit derivatives CDS (Credit Default Swaps), CMO (Collateralized Mortgage Obligations), CDO (Collateralized Debt Obligations) are OTC contracts, blamed for the 2008 financial crisis. There are also exchange-traded credit derivatives (eg itraxx). Caps, floors, collars A cap is an OTC interest rate derivative. Could use it to limit exposure to climbing rate. Eg. if I m paying interest on a floating rate loan, I might buy a cap that pays me P(R t R) + each quarter. P = principal, R t = 3 month LIBOR that quarter, R = cap rate (ie. like the strike). A floor is the same, but limits exposure to falling rates. A collar limits exposure to big changes either way.
Option-like contracts [Apr 5] Swaptions An option to enter into an interest rate swap at time T at swap rate K. Buyer exercises if the swap rate at time T is > K. Otherwise not (since could buy the swap for less at the market rate). Employee stock options Executive compensation: American calls on the company stock. Are supposed to incentivize executives to the stock price. Embedded bond options Callable (corporate) bonds: Issuing firm has an option to buy the bond back at a specified price Convertible (corporate) bonds: Bondholder has an option to convert the bond into company stock.
Other uses of options [Apr 5] ETF s Many Exchange traded funds are like low-cost mutual funds, traded on exchanges rather than by unit purchase/redemption from the issuer. There are also versions with complex valuation (leveraged, inverse), often realized by engineering payoffs via derivatives. Embedded options & retirement savings Variable Annuities are retirement savings products issued mainly by insurance companies. Early versions (in Canada) were known as segregated mutual funds. Essentially a mutual fund + some kind of option. Eg. GMDB (Guaranteed Minimum Death Benefit) essentially a put option at death, which guarantees that heirs will at least receive the initial deposit back.
Variable annuities (cont d) [Apr 5] Eg. GMWB (Guaranteed Minimum Withdrawal Benefit), or GLWB (Guaranteed Lifetime Withdrawal Benefit) ensures that income stream in retirement won t fall below a certain level. Essentially an option to convert the mutual fund to a life annuity, if the assets in the fund are ever exhausted. A good portion of my own finance work involves pricing, hedging, and client management of these options. (Joint work with H. Huaxiong, M.A. Milevsky)