We would like to compute d(S T X) + , where S t follows the Geometric Brownian

Question:

We would like to compute d(S_T −X)⁺, where S_t follows the Geometric Brownian process

d St St = = (r - q) dt+o (St, t) dZt. The function (S_T − X)⁺ has a discontinuity at S_T = X. Rossi (2002) proposed to approximate (S_T − X)⁺ by the following function f (S_T) whose first derivative is continuous, where

f(ST) = 0 (ST-X) 2 ST-X- 2 if ST < X if X ST < X+. if ST if ST X +

Here, є is a small positive quantity. By applying Ito’s lemma, show that

f(ST) = f(So) + T T 1 fo f" (St) dSt + 5 + 2/2 o (St, t)s f" (S) dt. - 0 By taking the limit 0, explain

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Mathematical Models Of Financial Derivative

ISBN: 9783642447938

2nd Edition

Authors: Yue-Kuen Kwok

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Question Posted: Dec 02, 2023 03:57 AM

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We would like to compute d(S T X) + , where S t follows the Geometric Brownian

Question:

d St St = = (r - q) dt + o (St, t) dZt.

Step by Step Answer:

The problem involves mathematical derivations and limits using stochastic calculus concepts like ...View the full answer

Mathematical Models Of Financial Derivative

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