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A stock price is currently $60. Over each of the next two three-month periods it is...

A stock price is currently $60. Over each of the next two three-month periods it is expected to up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $61

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Expert Solution

There are three parameters of Option Binomial Pricing Model

  • up factor (u)
  • down factor (d)
  • probability (P)

up factor and down factor used to calculate rise in price and fall in price of underlying assets in one period. Probability is measure probability of rise in price and (1-P) is probability of price fall.

Risk-neutral Probability of rise in price can be calculated with following formula -

where,

UP = up price

LP = Low price

Probability for fall in price = (1-P)

Pay off of call option = Max(stock price - Strike Price,0)

Please refer to below spreadsheet for calculation of European call option under two-step binomial Pricing model -

Formula reference -

Thus, value of six month European call option is $ 2.03 (rounded to two decimal)


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