Theta of a call option formula
Financial acronyms
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Description of the Theta of a call option formula
Formula for the calculation of the theta of a call option. Theta measures the option value's sensitivity to the passage of time.
Formula
\[ \theta = -\frac{S\phi\left ( d1 \right )\sigma}{2\sqrt{t}}-rKe^{-rt}N\left ( d2 \right ) \\ {\small where: \phi\left ( d1 \right ) = \frac{e^{-\frac{x^{2}}{2}}}{\sqrt{2\pi}} } ; \] \[ {\small d1 = \frac{ln \left( \frac{S}{K} \right ) + \left(r+\frac{\sigma^{2}}{2}\right)t}{\sigma\sqrt{t}} ; } \] \[ {\small d2 = d1 - \sigma \sqrt{t}} \ \]
Symbols
\(K\ \)
Option strike price
\(N\ \)
Standard normal cumulative distribution function
\(r\ \)
\(σ\ \)
Volatility of the underlying
\(S\ \)
Price of the underlying
\(t\ \)
Time to option's expiry
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