Let the price process XY (t) follow the geometric Brownian motion and let K be a general positive…

Let the price process XY (t) follow the geometric
Brownian motion   

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 and let K be a general positive constant.

(a) What is the price of a contract that pays a unit of Y
when XY (T ) ≥ K when T → ∞? How would you hedge such a
contract?

(b) What is the price of a contract that pays a unit of X
when XY (T ) ≥ K when T → ∞? How would you hedge such a
contract?

(c) Determine the price and the hedge of a European call
option with the payoff (XT − K · YT ) + when

T → ∞.

 

Chapter 4 Interest
Rate Contracts