I'm looking at the solutions to the final part of this question and am getting a bit confused. The expectation under Q of the value of the derivative is taken as the payoff (10) multiplied by the formula in the tables for the Probability of ((max(Bs + mus) > 1.44). Is this not a real world formula for the probability? Why can you take the Q probability as being the exact same number as the P probability, or am I misunderstanding something? Thanks
The formula in Section 7.2 of the Tables applies to standard Brownian Motion, Bs. If Bs is standard Brownian Motion with respect to real-world probabilities P, then the probability obtained from the formula would be a real-world probability. If Bs is standard Brownian Motion with respect to risk-neutral probabilities Q, then the probability obtained from the formula would be a risk-neutral probability. Unusually in this question, the probability measure isn't stated explicitly. But there's no mention of real-world probabilities at all, and the formula you've written down in (ii) is in terms of risk-neutral probabilities, so I'd say the most obvious assumption to make was that Bs was standard Brownian motion with respect to Q, so the formula yields the risk-neutral probabilities required.
i think there is also a printing mistake in the final solution given. the sign of 2u in the first cumulative function must be positive while in the second cumulative function it should be negative .am i right?
