Question

1. Answer three parts of this question. Your answers for each part should be no more than two pages long. (a) Both European put and call options can be used to provide portfolio insurance. Explain the strategies required for each option and show that they are equivalent. (b) ‘American call options should never be exercised early’. Critically evaluate this statement, providing proofs of your arguments where necessary. (c) Holding all other factors constant, what happens to the price of European put and call options when the price volatility of the underlying asset decreases? Fully explain your answer. (d) Describe how to construct an option trading strategy that will deliver a certain outcome at maturity. (e) In the Binomial Model of Option Pricing, the risk neutral probability of an upward movement in the underlying stock price will be different for two identical stocks if one pays a dividend and the other does not. Is this statement true, false or uncertain? Explain your answer fully.

Answer 1

a)

A European call option gives the owner the liberty to acquire the underlying security at expiry. A call option buyer is bullish on the underlying asset and expects the market price to trade higher than the call option's strike price before or by the expiration date. The option's strike price is the price at which the contract converts to shares of the underlying asset. For an investor to profit from a call option, the stock's price, at expiry, has to be trading high enough above the strike price to cover the cost of the option premium.

A European put option allows the holder to sell the underlying security at expiry. A put option buyer is bearish on the underlying asset and expects the market price to trade lower than the option's strike price before or by the contract's expiration. For an investor to profit from a put option, the stock's price, at expiry, has to be trading far enough below the strike price to cover the cost of the option premium.

Closing a European Option Early

Typically, exercising an option means initializing the rights of the option so that a trade is executed at the strike price. However, many investors don't like to wait for a European option to expire. Instead, investors can sell the option contract back to the market before its expiration.

Option prices change based on the movement and volatility of the underlying asset and the time until expiration. As a stock price rises and falls, the value—signified by the premium—of the option increases and decreases. Investors can unwind their option position early if the current option premium is higher than the premium they initially paid. The investor would receive the net difference between the two premiums.

Closing the option position, before expiration means the trader realizes any gains or losses on the contract itself. An existing call option could be sold early if the stock has risen significantly while a put option could be sold if the stock's price has fallen.

Closing the European option early depends on the prevailing market conditions, the value of the premium—its intrinsic value—and the option's time value. The amount of time remaining before a contract's expiration is the time value. The intrinsic value is an assumed price based on if the contract is in-, out-, or at-the-money. It is the difference between the stated strike price and the market price of the underlying asset. If an option is close to its expiration, it's unlikely an investor will get much return for selling the option early, because there's little time left for the option to make money. In this case, the option's worth rests on its intrinsic value.

Example of a European Option

An investor purchases a July call option on Citigroup Inc. (C) with a $50 strike price. The premium is $5 per contract—100 shares—for a total cost of $500 ($5 x 100 = $500). At expiration, Citi is trading at $75. In this case, the owner of the call option has the right to purchase the stock at $50—exercise their option—making $25 per share profit. When factoring in the initial premium of $5, the net profit is $20 per share or $2,000 (25 - $5 = $20 x 100 = $2000).

Let's consider a second scenario whereby Citigroup's stock price fell to $30 by the time of the call option's expiration. Since the stock is trading below the strike of $50, the option isn't exercised and expires worthlessly. The investor loses the premium of $500 paid at the onset.

The investor can wait until expiry to determine whether the trade is profitable, or they can try to sell the call option back to the market. Whether the premium received for selling the call option is enough to cover the initial $5 paid is dependent on many conditions including economic conditions, the company's earnings, the time left until expiration, and the volatility of the stock's price at the time of the sale. There's no guarantee the premium received from selling the call option before expiry will be enough to offset the $5 premium paid initially.

b)

Early exercise happens when the owner of a call or put invokes his or her contractual rights before expiration. As a result, an option seller will be assigned, shares of stock will change hands, and the result is not always pretty for the seller.

Being required to buy or sell shares of stock before you originally expected to do so can impact the potential risk or reward of your overall position and become a major headache. But chances are, if you sell options — either as a simple position or as part of a more complex strategy — sooner or later, you’ll get hit with a surprise early assignment. Many traders fail to plan for this possibility and feel like their strategy is falling apart when it does happen.

The strategies that can be messed up the most by early assignment tend to be multi-leg strategies like short spreads, butterflies, long calendar spreads and diagonal spreads. The latter two strategies can go particularly haywire as a result of early assignment, because you’re dealing with multiple expiration dates.

In most cases, it’s a bad idea for option owners to exercise early. However, there are a few instances when exercising early does make sense.

Three Reasons Not to Exercise Calls Early

1. Keep Your risk LImited

2. Save Your Cash

3. Don't miss out on Time Value

The exception to these three rules occurs when a dividend is going to be paid on the stock. Call buyers are not entitled to dividend payments, so if you want to receive the dividend, you have to exercise the in-the-money call and become a stock owner.

If the upcoming dividend amount is larger than the time value remaining in the call’s price, it might make sense to exercise the option. But you have to do so prior to the ex-dividend date.

c)

Option Pricing Models

Before venturing into the world of trading options, investors should have a good understanding of the factors determining the value of an option. These include the current stock price, the intrinsic value, time to expiration or the time value, volatility, interest rates, and cash dividends paid.

Volatility

An option's time value is also highly dependent on the volatility the market expects the stock to display up to expiration. Typically, stocks with high volatility have a higher probability for the option to be profitable or in-the-money by expiry. As a result, the time value—as a component of the option's premium—is typically higher to compensate for the increased chance that the stock's price could move beyond the strike price and expire in-the-money.

One of the metrics used to measure volatile stocks is called beta. Beta measures the volatility of a stock when compared to the overall market. Volatile stocks tend to have high betas primarily due to the uncertainty of the price of the stock before the option expires. However, high beta stocks also carry more risk than low-beta stocks. In other words, volatility is a double-edged sword, meaning it allows investors the potential for significant returns, but volatility can also lead to significant losses.

Basically, when the market believes a stock will be very volatile, the time value of the option rises. On the other hand, when the market believes a stock will be less volatile, the time value of the option falls. The expectation by the market of a stock's future volatility is key to the price of options.