If I have only strike, call and put prices for European options, how do I work towards computing the continuous dividend yield?
2 Answers
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Suppose you have a call/put pair with the same strike $K.$ Then a position long the call and short the put has the payoff of a forward struck at $K:$ $$C(K) - P(K) = e^{-rT} \mathbb{E}[ S(T) - K ],$$ Where $C(K)$ and $P(K)$ are the call and put price, $r$ is the interest rate, and $T$ is the time to expiry. Then by linearity of expectation and the martingale property $$ \mathbb{E}[ S(T) ] = e^{(r-q)T}S(0),$$ we can solve for dividend rate $q.$
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$\begingroup$ Thanks! But isn't r The risk free rate there? $\endgroup$– user15941Commented Apr 15, 2015 at 21:09
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Consider two different strikes $K_1$ and $K_2$. Then, for $i=1$ and $2$, \begin{align*} C(K_i)-P(K_i) &= e^{-r T}E(S_T-K)\\ &=e^{-qT}S_0 - e^{-rT}K_i. \end{align*} Now, the two unknown parameters $r$ and $q$ can be solved from the two equations.
