Question

A stock is currently priced at $52.00. The risk free rate is 4.6% per annum with continuous compounding. In 5 months, its price will be $60.84 with probability 0.57 or $44.72 with probability 0.43. Using the binomial tree model, compute the present value of your expected profit if you buy a 5 month European call with strike price $57.00. Recall that profit can be negative.

Answer 1

• Profit if price increases = 60.84 - 57 = $3.84
• Probability of price increasing = 57%
• Loss if price falls = 52 - 44.72 = $7.28
• Probability of price fall = 43%
• Risk-free rate = 4.6%; thus:
  i = 1 + (r x t) = 1 + (0.046 x 5/12) = 1.01917, or
  i = (1+0.046) + [(0.046 x 0.046) / 2]^5/12 = 1.01934 [This is more accurate]
• Present Value of expected profit = ($3.84 x 57% - $7.28 x 43%) / 1.01917 = -$0.92. [It is negative]
  Or ($3.84 x 57% - $7.28 x 43%) / 1.01934 = -$0.92 [It is negative]