Question

A share price is currently £120. It is known that in 6 months' time it will be either t06 or 1141 . The rik tree interet rate a 10% per annum. Let P be the wive of a 6 moneh furestin put orson with an exercise price of f120.

(a) Letting P denote the risk-neutal probability,

Pᵢ = P(Sₒ∗,T) and
P​ =P(S d,T), caicalale P= Please give your answer as a decimal (not a percentage) with ot least 2 decimal ploces
Pᵤ = P=&
​(b) What is the (arbitrage free) initial price of P ?
Pₐ = f Please give yout antwer corect to 2 decimal places. (c) Let B be a bond with face value 48.8 and maturity in 6 months time. Which has hager value at ℓ−0 ? fr mand

Answer 1

To calculate the risk-neutral probability, use the formula P = (S - X)/(S_u - S_d). The risk-neutral probability P is 0. The initial price of the put option Pₐ is 0. A bond with a face value of £48.8 and maturity in 6 months' time will have a higher value if the interest rate is lower.

Step-by-step explanation:

To calculate the risk-neutral probability, we need to use the formula:
P = (S - X)/(S_u - S_d)
where S is the current share price (£120), X is the exercise price (£120), S_u is the share price at t06 (£141), and S_d is the share price at 114 (£114).

Using the given values, we have:
P = (120 - 120)/(141 - 114) = 0

Therefore, the risk-neutral probability P is 0.

The initial price of the put option can be calculated using the risk-neutral probability P:
Pₐ = (Pᵢ - P)/(1 + r)
where Pᵢ is the risk-neutral probability (0), P is the risk-neutral probability (0), and r is the annual risk-free interest rate (10%).

Substituting the values, we have:
Pₐ = (0 - 0)/(1 + 0.10) = 0

Therefore, the initial price of the put option Pₐ is 0.

A bond with a face value of £48.8 and maturity in 6 months' time will have a higher value if the interest rate is lower. The bond's price will increase as the interest rate decreases.