《Arbitrage Theory in Continuous Time 2rd-Solutions》.pdf

Suggested Solutions for Finance II Fall 2004 Irina Slinko (From the Solutions Manual of Raquel M. Gaspar) 1 Contents 4 Stochastic Integrals 3 5 Differential Equations 7 7 Arbitrage Pricing 9 8 Completeness and Hedging 15 9 Parity Relations and Delta Hedging 17 13 Several Underlying Assets 21 16 Incomplete Markets 24 17 Dividends 25 18 Currency Derivatives 27 20 Bonds and Interest Rates 30 21 Short Rate Models 33 22 Martingale Models for the Short Rate 35 23 Forward Rate Models 39 24 Change of Numeraire 42 2 4 Stochastic Integrals Exercise 4.1 (a) Since Z (t) is determinist, we have dZ (t) = αeαt dt = αZ (t)dt. (b) By definition of a stochastic differential dZ (t) = g (t)dW (t) (c) Using Itˆo’s formula 2 α αW (t) αW (t) dZ (t) = e dt + αe dW (t) 2 2