Finance calculation problem involving income in various worlds, needs to be disc
ID: 2647558 • Letter: F
Question
Finance calculation problem involving income in various worlds, needs to be disccussed in four different ways.
The variable S is an investment asset providing income at the rate q measured in currency A and it follows the process: In the real world. Defining new variables as necessary, give the process followed by S, and the corresponding market price of risk, in: A world that is the traditional risk-neutral world for Currency A A world that is the traditional risk-neutral world for Currency B A world that is forward risk-neutral world with respect to a zero-coupon currency A bond maturing at time T A world that is forward risk-neutral world with respect to a zero-coupon currency B bond maturing at time TExplanation / Answer
Answer: (1.) In the traditional risk- neutral world the process followed by S is:
dS= ( r- q )S dt +?s S dz
Where r is the instantaneous risk-free rate.The market price of dz-risk is Zero.
(2.) In the traditional risk- neutral world for currency B the process is
dS= ( r- q +PQS?S?Q )S dt +?s S dz
Where Q is the exchange rate (units of A per unit of B),?Q is the volatility of Q and PQS is the coefficient of correlation between Q and S. The market price of dz- risk is PQS?Q.
(3) In a world that is forward risk - neutral with respect to zero-coupon currency A maturing at time T
dS= ( r- q +?S?P)S dt +?s S dz
Where ?P is the bond price volatility. The market price of dz- risk is ?P.
(4) In a world that is forward risk - neutral with respect to zero-coupon currency B maturing at time T
dS= ( r- q +?S?P+PFS?S?F)S dt +?s S dz
Where F is forward exchange rate, ?F is the volatility of F (units of A per unit of B, and PFS is the correlation between F and S. The market price of dz- risk is ?P +PFS?F..
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