Problem 4. (i) Verify that is a solution of the Black-Scholes partial differential equation Si+rSfs+5o*s®fss = rf 1

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Problem 4. (i) Verify that
S(S.t) = (ar+3o")(r-ngs
is a solution of the Black-Scholes partial differential equation
1
with f(0, t) - 0 for 0SIST and f(Sr.T) S;
(i) Consider a derivative with underlying asset whose price S follows the Ito process
ds - uSdt + aSdB and which provides a single payoff at time T > 0 in the
amount of S, where Sr is the underlying asset price at time T. What is the
price of this derivative at time 0<t< T? (Hint: The answer is not far away.)
Transcribed Image Text:Problem 4. (i) Verify that S(S.t) = (ar+3o")(r-ngs is a solution of the Black-Scholes partial differential equation 1 with f(0, t) - 0 for 0SIST and f(Sr.T) S; (i) Consider a derivative with underlying asset whose price S follows the Ito process ds - uSdt + aSdB and which provides a single payoff at time T > 0 in the amount of S, where Sr is the underlying asset price at time T. What is the price of this derivative at time 0<t< T? (Hint: The answer is not far away.)
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