Question

Draw the tree for a put option on $20,000 with a strike price of £10,000. the current exchange rate is £1.00 = $2.00 and in one period the dollar value of the pound will either double or be cut in half. the current interest rates are i$ = 3% and are i£ = 2%. multiple choice none of the options both of the options

Answer 1

$ 0.000912 / pound

Step-by-step explanation:

Current spot rate : 100 pound / $ or 0.01 $ / pound

In the next period the $ value of the pound can either increase or decrease by 15%

$ Risk-free rate = 5% and

pound Risk-free rate = 1%

Net Risk- free Rate = 5 - 1

= 4%

Risk-Neutral Probability of price Rise (p) = (0.04 - 0.085) / (1.15 - 0.85)

= 0.653

$ price of pound if price rises = 1.15 x 0.01 =$ 0.0115 / pound

$ price of pound if price falls = 0.85 x 0.01 = $ 0.0085 / pound

Strike price = current spot rate (as option is at the money) = 0.01 $ / pound

Therefore, pay offs one period later

if price is $ 0.0115 / pound, pay off (p₁)= 0.0115 - 0.01

= 0.0015$/ Pound

If price is 0.0085 $ / pound, pay off (p₂) = $0

Hence, Expecyed pay off = p₁ x p + p₂ x (1-p)

= 0.0015 x 0.633 + 0 x ( 1 - 0.633)

= $ 0.00095 / pound

Call price = Present value of Expected pay off at Net Risk-free risk

= 0.00095 exp (0.04)

= $ 0.000912 / pound