Solution manual for an introduction to the mathematics of financial derivatives second edition
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Solution manual for an introduction to the mathematics of financial derivatives second edition
l. (a) Payoff diagram at expiration:CHAPTERlFIGURE 0.1 Payoff diagram for both a short sale of stock and an at-the-money call.Payoff diagram at expira Solution manual for an introduction to the mathematics of financial derivatives second edition ation:FIGURE 0.2 Payoff diagram for a long put with strike K| and a tong call with strike K-. Kị < KịPayoff diagram at expiration:FIGURE 0.3 Payoff diagram for a (long put/short call) combination at Kt plus a (long call/short put) combination at Kĩ > Kt.(b) Payoff diagram before expiration:FIGURE 0. Solution manual for an introduction to the mathematics of financial derivatives second edition 4 Pre-maturity payoff diagram for both a short sale of stock and an at-the-money call.Payoff diagram before expiration:FIGURE 0.5 Pre-maturity payoffSolution manual for an introduction to the mathematics of financial derivatives second edition
diagram tor a long put with strike Ki and 3 long call with strike Ki. AI < A;.iiiPayoff diagram before expiration:FIGURE 0.6 Pre-maturity payoff diagrl. (a) Payoff diagram at expiration:CHAPTERlFIGURE 0.1 Payoff diagram for both a short sale of stock and an at-the-money call.Payoff diagram at expira Solution manual for an introduction to the mathematics of financial derivatives second edition swap and L|2 and £|8 the USD Libor rate at 12 months and 18 months respectively. The cash flows are given by12 months 18 months 24 monthsFloating leg +jV+jV X Ạp +jV X (1 + ty)Fixed leg-jV-JV X -jV X (1 +where the 1 in the 24 months column represents the notional amount.(b)If one had a floating rate Solution manual for an introduction to the mathematics of financial derivatives second edition obligation and wished to pay a fixed rate, K. then enter into two FRA contracts at rate K with maturity 18 and 24 months. For example, at 18 months,Solution manual for an introduction to the mathematics of financial derivatives second edition
if the floating rate were above K, then the FRA would be in-the-money by precisely the amount required to offset, the higher floating rate payment. Thl. (a) Payoff diagram at expiration:CHAPTERlFIGURE 0.1 Payoff diagram for both a short sale of stock and an at-the-money call.Payoff diagram at expira Solution manual for an introduction to the mathematics of financial derivatives second edition s the appropriate interest rate options are available. A long position in an interest rate cap at rate K and a short position in an interest rate floor at rate K, both maturing on the floating rate payment date, ensure that a fixed rate of K is paid. If the floating rate, say r-/ , is above K at exp Solution manual for an introduction to the mathematics of financial derivatives second edition iry, a net payment at rate K is required after taking into account, the value of the cap. .V X (r-/- - k). If the floating rate is below K at expiry,Solution manual for an introduction to the mathematics of financial derivatives second edition
say Ft, then a payment at rate Ff must be made on the floating rate obligation. However, the short position in the floor requires an additional paymenl. (a) Payoff diagram at expiration:CHAPTERlFIGURE 0.1 Payoff diagram for both a short sale of stock and an at-the-money call.Payoff diagram at expira Solution manual for an introduction to the mathematics of financial derivatives second edition r 1 ton of wheat, s is the annual insurance cost, for 1 ton of wheat, and r is the simple interest rate. If Ft > (Sj 4-c + s)(l +r), then construct the following arbitrage portfolioPositionPayoff at tPayoff at TShort futures0Ft - StBorrow St + c+ K+(Sr + c + s)-(St + c + *)(l + r)Buy wheat and pay s Solution manual for an introduction to the mathematics of financial derivatives second edition torage, insurance costs—(St + c + s)StTotal0Fl - {St + c + s)( 1 + r) > 0Thus. Ft <+ c + s)(l + r). If Ft < {St + c + s)( 1 + r), one cannot immediateSolution manual for an introduction to the mathematics of financial derivatives second edition
ly reverse theholdings in the above portfolio to create another arbitrage portfolio. A problem arises since wheat, is not typically held as an investml. (a) Payoff diagram at expiration:CHAPTERlFIGURE 0.1 Payoff diagram for both a short sale of stock and an at-the-money call.Payoff diagram at expira Solution manual for an introduction to the mathematics of financial derivatives second edition ensues with Ft > Sf(l + r) but not Ft > {St + c + s)(l + r). If the asset were of a financial nature or a commodity held for investment such as gold, one could sell the asset, and save on the storage and insurance costs. These assets produce an exact relationship, Ft = (5/ + r + a)(l + r). Holding Solution manual for an introduction to the mathematics of financial derivatives second edition an asset such as wheat has value since it may be consumed. For instance, a large bakery requires wheat for production ami maintains an inventory. ThesSolution manual for an introduction to the mathematics of financial derivatives second edition
e companies would be reluctant to substitute a futures contract for the actual underlying. Hence, the price of a futures is allowed to be less than (Sl. (a) Payoff diagram at expiration:CHAPTERlFIGURE 0.1 Payoff diagram for both a short sale of stock and an at-the-money call.Payoff diagram at expira Solution manual for an introduction to the mathematics of financial derivatives second edition Invest. St -St +5r(l + r)Sell wheat+.$i-StTotal0s,(l + r) - Ft > 0l. (a) Payoff diagram at expiration:CHAPTERlFIGURE 0.1 Payoff diagram for both a short sale of stock and an at-the-money call.Payoff diagram at expiraGọi ngay
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