Why do you think p is called the ‘risk-neutral probability’ of S going up?.

Risk-neutral probability

Consider the one-step binomial model over the period [0, T]. Let ω^{(u)} denote the ‘up’ scenario and ω^{(d)} the ‘down’ scenario with respective probabilities p^{(u)} and p^{(d)} = 1 – p^{(u)}. The underlying asset S is worth St at any point in time t and does not pay any dividend. Let Dt be the value of a derivative on S at time t, r the annual risk-free rate and denote the compound interest rate over the period [0, T].

Assume that the final price of the underlying is:

• in the ‘up’ scenario;

• in the ‘down’ scenario,

where u and d are parameters satisfying:

(a) In this question Calculate the value of a European call struck at 100. Does your result depend on the probabilities and ?

(b) In general, show that the value of the derivative at time t = 0 can be written:

where p is a function of r^{[T]} , u and d.

(c) Verify that

(d) Let

(i) Verify that D_{0} is equal to the expected present value of the payoff D_{T}.

(ii) Find the expected gross rate of return on S over [0, T]. Why do you think p is called the ‘risk-neutral probability’ of S going up?

The post Why do you think p is called the ‘risk-neutral probability’ of S going up? appeared first on Best Custom Essay Writing Services | EssayBureau.com.

Why do you think p is called the ‘risk-neutral probability’ of S going up?