5.05.2005

Q&A: What's the expiration-day P&L of the covered call position if...

...an investor buys a share of stock for $20, and simultaneously sells a call option on that stock for $5? The exercise price of the call is $30, the call will expire in 3 months, and the stock finishes at $18? What if the stock price finishes at $32? $40?

CppQuant Answer

  • the portfolio costs $20 - 5 = $15
  • if stock price finishes at $18: the value of the covered call = $18 (the value of the stock) + $5 (the option premium) = $23. P&L = 23 - 15 = $8
  • if $32: the buyer will exercise the option = $30 + $5 = $35. P&L = 35 - 15 = $20
  • $40: same as above.

Bonus Points

  • Value of covered call = value of underlying + value of short call
  • Valueof the underlying = MAX(0, ST - X) = ST if ST <= X, or X if ST > X.

Category: C++ Quant > Derivatives > Options

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