Question

The current futures price of a stock is $15 per share. One month later, when the futures option expires, the futures price could have risen to $16.5 per share or declined to $14 per share. The strike price is $14.5. The risk-free rate is 6%.

What is the value of the risk-free portfolio at the maturity?

Answer 1

Risk neutral probability = ( R - d) / ( u -d)

R = ( 1 + risk free rate ) = 1.06

u = upmove / current price = 16.50/15 = 1.10

d = downmove / current price = 14/15 = 0.93

Risk neutral probability =p=(R - d) / ( u -d)

= ( 1.06 - 0.93 ) / ( 1.10 - 0.93)

= 0.76

1 -p = 1 - 0.76 = 0.24

payoff from call option = Max [ Futures price - exercise price, 0 ]

payoff in upmove = 16.50 - 14.50 = 2.00

payoff in downmove = 0 as the futures price is less than exercise price

expected payoff = 0.76 * 2 + 0.24 * 0 = 1.52

value of the risk-free portfolio at the maturity = $1.52