Q&A: What's the price of the options using Black-Scholes-Merton model

Consider call and put options with a common exercise price of $100 and 150 days until expiration. The underlying stock trades for $102, and that you expect the stock to pay a $3 dividend in 90 days. The continuously compounded interest rate is 9%, and the standard deviation for the stock is 0.30.

A: Anything that affects the underlying price at expiration will affect the price of the option. use S0 - PV(CF, 0, T) in the Black-Scholes-Merton model instead of S0 to adjust for cash flows of the underlying.

  • The $3 dividend PV = $3*e^( -9%*(90/365)) = $2.93. In Excel, this can be done with EXP() function.
  • The adjusted stock price = $102 - $2.93 = $99.07
  • Apply the Black-Scholes-Merton model
BSM Call Put
Adjusted for dividends 8.91 6.21
Unadjusted 10.74 5.11
  • The difference in prices is substantial, amounting to almost 20%.

Bonus Points

  • Adjusting the stock price reduces the value of the call and increases the value of the put.

Category: C++ Quant > Derivatives > Valuation

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