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Unformatted text preview: 15-1CHAPTER 15: ADVANCED DERIVATIVES AND STRATEGIESEND-OF-CHAPTER QUESTIONS AND PROBLEMS1.In both types of swaps there are two parties who make payments to each other at specific dates accordingto different formulas. In an interest rate swap the payments made by one party are based on a particularinterest rate. The other payments can be fixed or based on another type of interest rate. In an equity swapthe payments of at least one party are based on the performance of a stock or index. The payments of theother party can be based on the performance of a different stock or index or can be based on a fixed orfloating interest rate. Thus, any swap in which one party's payments are based on a stock or index iscalled an equity swap even though it might really be only part-equity and part-interest rate.2. Most structured notes are tailored, i.e., structured, to the specific needs of an investor. A portfoliomanager whose portfolio is exposed to loss from falling interest rates over the holding period mightpurchase an inverse floating rate note as a type of hedge. If interest rates decrease, the inverse floater willgain, thereby offsetting some or all of the loss on the rest of the portfolio. Of course, the inverse floaterwill lose if rates rise thereby offsetting some or all of the gain on the rest of the portfolio. 3. The payoffs at expiration from the chooser are as follows:Payoff of Chooser at ExpirationChoice made at tSTEST> Edesignate chooser as a callST- Edesignate chooser as putE - STThe holder of the chooser option will designate it as a call at time t if C(St,T-t,E) > P(St,T-t,E). From put-call parity, the put price can be expressed as C(St,T-t,E) - St+ E(1 + r)-(T-t). Thus, C(St,T-t,E) > P(St,T-t,E) implies that C(St,T-t,E) > C(St,T-t,E) - St+ E(1 + r)-(T-t), which implies that St> E(1 + r)-(T-t). We are told that to replicate the chooser we hold a call expiring at T with exercise price E and a putexpiring at t with exercise price E(1 + r)-(T-t). Now suppose we are at t and the following occurs:St> E(1 + r)-(T-t)The call is still alive but the put expires out-of-the-money. At the calls expiration at T, it willpay off ST- E if ST> E and zero otherwise, which is exactly like the chooser.StE(1 + r)-(T-t)The call is still alive and the put expires and pays off E(1 + r)-(T-t)- ST. Take the amount E(1 + r)-(T-t)and invest it in risk-free bonds. At T, it will be worth E. Short the stock at t and buy it backat T. Thus, the overall value at T if ST> E is ST- E (from the call) + E (from the risk-free bond)- ST(from buying back the stock), for a total of 0. If at T STE then you will have zero (fromthe call), E (from the risk-free bond) and - ST(from buying back the stock), for a total of E - ST....
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