Let the dynamics of the short rate r(t) be governed by the extended Vasicek model Show that

Question:

Let the dynamics of the short rate r(t) be governed by the extended Vasicek model

dr (t) = [p(t) - ar(t)] dt+ or dZ(t).

Show that the value of the European call option with strike price X maturity at T on a T’-maturity discount bond is given by

c(t; T, T')= B(t, T')N (d) - XB(t, T)N(d),

where B(t,T ) is the discount bond price,

d = 1 In B(t, T') XB(t, T) or = = [1 - e-(T- + -T) Nja) 2 d=d - 6, 1-e-2a (T-t) 2

Also, show that the put-call parity relation between the prices of the European put and call options on the same underlying discount bond is given by

c(t; T, T') + XB(t, T) = p(t; T, T') + B(t, T').

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Related Book For answer-question

Mathematical Models Of Financial Derivative

ISBN: 9783642447938

2nd Edition

Authors: Yue-Kuen Kwok

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Question Posted: Nov 30, 2023 07:31 AM

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Let the dynamics of the short rate r(t) be governed by the extended Vasicek model Show that

Question:

dr (t) = [p(t) - ar(t)] dt+ or dZ(t).

Step by Step Answer:

a European Call Option Price The value of a European call option with strike price X and maturity T ...View the full answer

Mathematical Models Of Financial Derivative

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