Consider a security market that contains one bond with price Pt and one stock with price...

 

 

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Consider a security market that contains one bond with price Pt and one stock with price St. Their dynamics are described by: (dPt = rPt dt, t≥ 0, PO = p. (dSt = µStdt + oSt dWt, t≥ 0, S0 = x. Suppose that an agent sells a European option on the stock St at price Yt and then invests it in the market. Assume that at each time the agent invests a portion of the amount Yt given by At into the stock, and the rest (Yt-At) into the bond. Now the agent has a portfolio based on the two securities. a) Derive the BSDE for pricing European options based on the portfolio above. b) Using the Feynman-Kac formula, find the associated PDE. Consider a security market that contains one bond with price Pt and one stock with price St. Their dynamics are described by: (dPt = rPt dt, t≥ 0, PO = p. (dSt = µStdt + oSt dWt, t≥ 0, S0 = x. Suppose that an agent sells a European option on the stock St at price Yt and then invests it in the market. Assume that at each time the agent invests a portion of the amount Yt given by At into the stock, and the rest (Yt-At) into the bond. Now the agent has a portfolio based on the two securities. a) Derive the BSDE for pricing European options based on the portfolio above. b) Using the Feynman-Kac formula, find the associated PDE.

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a Before calculating the BSDE for pricing European options using the aforementioned portfolio it is ... View the full answer