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Estimating Continuous Dividend Yield from European Option Prices

Article Quant Q&A · Author: Done
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Summary

Put–call parity links prices of European calls and puts with the same strike to the value of a forward contract. With the risk-free rate and time to expiry known, the parity relationship gives the forward price and can be rearranged to infer the asset’s continuous dividend yield.

If the risk-free rate is also unknown, the document proposes using call–put pairs at two different strikes. The resulting equations contain both the interest rate and dividend yield, which can then be solved together. The method relies on European options and the stated pricing relationships; it does not discuss market frictions, quote noise, or how to handle inconsistent prices.

Key ideas

  • A call minus a put with the same strike replicates a forward payoff under put–call parity.
  • The forward relationship connects expected future asset value to spot price, interest rate, and dividend yield.
  • With a known interest rate, one matched call–put pair can be used to infer the continuous dividend yield.
  • With two strikes, the parity equations can be used to solve jointly for the interest rate and dividend yield.

Tags

OptionsDerivatives pricing
Full text
# Annual dividend yield using option prices


# Annual dividend yield using option prices












If I have only strike, call and put prices for European options, how do I work towards computing the continuous dividend yield?

## Answer by q.t.f. (score 1, accepted)

https://quant.stackexchange.com/a/17394

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 $q.$

## Answer by Gordon (score 0)

https://quant.stackexchange.com/a/17410

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.