1. Context
Here, we take a look at how option contracts are adjusted for stock dividends and stock splits. The details of the reading in which this topic appears are given below:
| Area | Financial Markets and Products |
| Reading | Mechanics of Option Markets |
| Reference | Hull, John, Ch10. Mechanics of Options Markets. In Options, Futures, and Other Derivatives, 9th Edition, Pearson, New York, 2014. |
2. Adjusting for Cash Dividends
Exchanges do not make any adjustment to option terms on account of cash dividends paid by underlying stocks. Stock prices do fall on ex-dividend dates on account of these dividends, and option values are affected. However, the impact of cash dividends is already priced into the premium that was paid for the option at the time of purchase. Some OTC options are dividend-protected (for cash dividends). If the firm declares a cash dividend, the strike price of such a dividend-protected option is reduced on the ex-dividend date by the amount of the dividend paid. This adjustment of strike price offsets the drop in the stock price owing the dividend and the option holder is unharmed.
3. Stock Dividends and Stock Splits
Instead of cash dividends, firms can elect to pay dividends in stock wherein current holder’s of the firm’s stock receive more stock in direct proportion to their current holdings. Further, in a $n$-for-$m$ stock split, the firm replaces every $m$ shares held by an investor by $n$ shares. The impact of both a stock dividend and splits is to increase the number of outstanding shares of the firm (and reduce the price of shares). A $q\%$ stock dividend can be effectively seen as a $(1+q)$-for-$1$ stock split.
4. Adjusting for Stock Splits
If the option’s terms are not accurately adjusted, stock splits alter it’s value radically. Consider a ATM call option on a stock that is currently trading at 200USD. If this stock were to undergo a 2-for-1 split it would bring down the price of the stock to 100USD (in an idealized scenario where factors such as additional interest in the stock / more liquidity do not affect the stock price) and double the number of shares. If the exercise price of the option were not adjusted, the call option would be worthless as it becomes virtually impossible for the stock price to exceed exercise price prior to maturity.
In general, a $n$-for-$m$ stock split takes the stock’s price (at time $t$) from $S_t$ to $\frac{m}{n}S_t$. The exchange makes the following adjustments to account for this split:
| Strike | $K \rightarrow \frac{m}{n}K$ |
| #Shares or #Options | $N \rightarrow \frac{n}{m}N$ |
The convention is increase the number of shares covered by each option (usually, 100 shares) in proportion to the stock dividend (i.e. a 15% stock dividend changes the number of shares from 100 to 115 and adjusts the exercise price by $1/1.15$). If the stock dividend or stock split results in new number shares being a multiple of 100, holders of outstanding option contracts are credited with more contracts. In either case, the effect is to alter the total number of shares received upon exercise. However, holding more number of options does affect transaction costs if you were to trade out of them prior to maturity.
5. Is the investor getting the promised payoff?
Yes, he is. We know that the original payoff to the investor (before the stock split or stock dividend) was given by:$$N\times\max\left( S_T – K, 0 \right)$$After the split and with the proposed adjustments, the payoff has now become:$$\left(\frac{n}{m}N\right)\times\max\left( \left( \frac{m}{n}S_T \right) – \left( \frac{m}{n}K \right), 0 \right)$$which is the same as before as algebraically the adjustments cancel out.
6. Does it affect the option’s current value?
No, it doesn’t. As we have seen above, the exercise (intrinsic) value of the option is unaffected by the stock split or stock dividends (thanks to the adjustments made by the exchange). Even the time value is not affected since the parameter which the time value relates to i.e. volatility is unaffected by stock splits. This is because the volatility that we input into a pricing model (such as Black Scholes) is the volatility of stock price returns (and not of stock price, the volatility of which will undoubtedly be affected by the split).
Owing to the $n$-for-$m$ stock split, as the stock price goes from $S_t$ to $\frac{m}{n}S_t$, it’s price volatility will go from $\sigma_S$ to $\frac{m}{n}\sigma_S$, but it’s return volatility $\sigma$ stays the same $\because \mbox{var}\left(\frac{\Delta\left(\frac{mS_t}{n}\right)}{\frac{mS_t}{n}}\right)=\mbox{var}\left(\frac{\Delta S_t}{S_t}\right)$
FAQs
If the firm declares a cash dividend, the strike price of such a dividend-protected option is reduced on the ex-dividend date by the amount of the dividend paid. This adjustment of strike price offsets the drop in the stock price owing the dividend and the option holder is unharmed.
What happens to options when a stock dividend? ›
Put options generally become more expensive because the price drops by the amount of the dividend (all else being equal). Call options become cheaper because of the anticipated drop in the price of the stock leading up to the ex-dividend date.
How do you adjust stock dividends? ›
Dividend Adjustment Calculation Details
The amount of the dividend is subtracted from the prior day's price; that result is then divided by the prior day's price. Historical prices are subsequently multiplied by this factor.
Are exchange listed options adjusted for the payment of an ordinary dividend? ›
Note, however, that not all exchanges make this adjustment. The U.S. exchanges do, but the Toronto Stock Exchange, for example, does not. On the other hand, stock options prices are usually not adjusted for ordinary cash dividends unless the dividend amount is 10% or more of the underlying value of the stock.
What is the option strategy for dividend stocks? ›
Dividend arbitrage is an options trading strategy that involves purchasing put options and an equivalent amount of underlying stock before its ex-dividend date and then exercising the put after collecting the dividend.
What is the formula for dividend adjustment? ›
Calculating Dividend Adjustments
For dividends the adjustment factor is calculated by subtracting the dividend from the close price the day before the ex-dividend date, and then dividing by that close price to get the adjustment factor in percentage terms.
What are the adjustments of option contracts? ›
An adjusted option exists when the original terms of the option contract are amended. Various types of corporate actions such as, stock splits, mergers, dividends, acquisitions, spin-offs or similar events relative to the underlying may cause an option to become adjusted.
Do options adjust for stock splits? ›
Stock splits are a common occurrence in company shares. They help reduce the price of a share to make it more affordable for investors. The total value of your shares does not change. Similarly, with an option on a stock, the option is adjusted so that the value does not change.
What happens to option price when dividend is paid? ›
Cash dividends affect option prices through their effect on the underlying stock price. Because the stock price is expected to drop by the amount of the dividend on the ex-dividend date, high cash dividends imply lower call premiums and higher put premiums.
What are dividend adjustments? ›
A dividend-adjusted return is a calculation of a stock's return that relies not only on capital appreciation but also on the dividends that shareholders receive. This adjustment provides investors with a more accurate evaluation of the return of an income-producing security over a specified holding period.
“Ordinary” cash dividends do not call for adjustments. An “ordinary” cash dividend is defined as one paid “pursuant to a policy or practice of paying such dividend on a quarterly or other regular basis.” A cash dividend which is considered to be outside this regular policy or practice is non-ordinary.
What is the stock dividend rule? ›
A stock dividend is a payment to shareholders that consists of additional shares rather than cash. The distributions are paid in fractions per existing share. For example, if a company issues a stock dividend of 5%, it will pay 0.05 shares for every share owned by a shareholder.
How are options adjusted for special dividends? ›
Most frequently, the strike price of your option will be adjusted lower to reflect the amount of the special dividend. For example, a one-time cash payment of $5 could turn your 25-strike call into a 20-strike call.
Is stock option the same as stock dividend? ›
Dividends offer an effective way to earn income from your equity investments. However, call option holders are not entitled to regular quarterly dividends, regardless of when they purchase their options. And, unlike stock or ETF prices, options contract prices are not adjusted downward on ex-dividend dates.
What is an example of an adjusted option? ›
An adjusted option may cover more or less than the usual 100 shares. For example, after a 3-for-2 stock split, the adjusted option will represent 150 shares. For such options, the premium must be multiplied by a corresponding factor. Example: buying 1 call (covering 150 shares) at 4 would cost $600.
How does a dividend affect a call option? ›
If a dividend is paid, it may lead to a decrease in the stock price, making it less likely that the call option will be exercised. Consequently, you might be able to keep the premium without having to sell your stock at the strike price.
How is Black Scholes adjusted for dividends? ›
Black-Scholes App
The calculator will adjust for the dividend by lowering the stock price by the present value of the expected dividend. In other words the stock price used in the formula will be: S0e-δT where δ is the expected annualized dividend yield. This assumes dividends are paid continuously throughout the year.
Do you get dividend if you have options? ›
First, it's important to understand that in strict terms, options don't pay dividends. Even if you own an option to purchase stock, you don't receive the dividends that the stock pays until you actually exercise the option and take ownership of the underlying shares.
