How Dividend Yield Can Reduce Long-Dated Call Values
Summary
The document addresses why extending an option’s time to expiry does not always increase a call’s value when the underlying has a positive dividend yield. Its explanation invokes the Black–Scholes call formula and put–call parity: as the horizon grows, dividends reduce the value attributable to the underlying stock, and sufficiently large cumulative distributions can erode the call’s value. The answer also compares dividend yield with the risk-free rate, noting that discounting dividends affects their impact.
This is an intuitive, asymptotic explanation rather than a general proof or a practical valuation procedure. The response’s simplified compounding discussion does not spell out all model assumptions, and the claim that the stock value tends toward zero depends on the continuous-yield framework and limiting setup. The document does not cover puts, early exercise, or how changing rates and dividend expectations affect a real option surface.
Key ideas
- A positive dividend yield can make longer time to expiry fail to increase a call’s value.
- Dividend distributions reduce the underlying value relevant to a call, while interest rates affect the discounted dividend impact.
- Put–call parity helps explain the limiting relationship between the stock’s value and a call’s value.
- The explanation relies on a simplified long-horizon argument and does not provide a general valuation method.
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Full text
# Time value of option not always leading to an increased option value # Time value of option not always leading to an increased option value My understanding was that as you increase the time to expiry of an option, the value of the option increases. However, I have run a bunch of scenarios and have realized that if you assume a dividend yield > 0%, the value of the option starts decreasing after x number of years. In other words, in the first z years, the value of the option increases, and after x years, it starts to decrease. This is even the case if the risk free rate > dividend yield. Can someone please explain to me intuitively why the dividend yield causes the value of the option to decrease after a certain number of years and why the time value of the option doesn't outweigh the effects of the dividend? Thanks very much. ## Answer by Thomas Baert (score 1) https://quant.stackexchange.com/a/18213 http://finance.bi.no/~bernt/gcc_prog/recipes/recipes/img169.png let $q t$ be big (t goes to infinity where q is the yield) and you will see why . The first part of the BS formula becomes zero. Also in accordance to put call parity, the call must be worth zero if the entire stock price has been paid out in dividends: http://en.wikipedia.org/wiki/Put%E2%80%93call_parity Dividends cause the stock price to call so if you pay out enough of them the price will be zero, hence C=0. If r>d then you must discount your dividends. (A 1% dividend isn't so great when the risk-free interest is 10%) If d>r then the dividends erode the call price more then interest boosts stock prices. Eventually you have a situation where r=d(discounted dividend). If d>r you can intuitively see how dividends would make calls worthless. When d=r it's harder to visualize, but consider 'interest' causes the price to be boosted by p(1+r) and then dividends cause it to fall p(1-d) so you have p=p(1+r)(1-d) since d=r and if you repeat this 100 or so times the (1-d^2)^100 part goes to zero and the expected value of the stock as time goes to infinity is zero. If r>d the discounting process on the dividend makes the above relation hold.
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