5.16.2005

Q&A: should the delta of a call option be close to...

... -1, 0, or 1 if it's on a stock trading at $100. The continuously compounding risk-free interest rate is 6%. The option has an exercise price of $50 and expires in one year. The standard deviation of the stock's returns is 0.1.

CppQuant Answer

Without no calculation, one knows its delta should be close to 1. The giveaway is the option is deep-in-the-money.

Bonus Points

  • When the underlying is at-the-money (ie. near the exercise price), delta is most sensitive to a change in the underlying price.
  • When the call/put option is deep-out-of-the-money, its delta approaches 0.
  • When the option is deep-in-the-money: Call delta approaches 1, Put delta approaches -1

Category: C++ Quant > Derivatives > Options

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