Vocabulary associated with Option

Vocabulary associated with Option.

The will use exercise the option only if it is profitable, otherwise, the option can be thrown away.

Followings are the vocabulary associated with the option:

Vocabulary associated with Option

Strike price:

The fixed price specified in the option contract at which the option holder can buy or sell the underlying asset can be defined as a strike or exercise price.

Exercising the option:

The transaction regarding buying or selling the underlying asset according to the option contract is called exercising the option.

Expiration date: The date on or before which the option can be exercised is called the expiration date.

American vs. European option: An option can be defined as an American option if it may be exercised anytime on or before the expiration date. A European option, on the other hand, can be defined as one which may be exercised only on the expiration date.

Option Premium

The option premium is the amount called the value of the option paid by the buyer to by the option. Some factors affect the premium of the option. A call option will yield a profit to the option holder if the current market price is greater than the exercise price.

The following outcomes may occur:

■ In-the-Money

The exercise price is less than the spot price of the underlying asset i.e., the current market price is greater than the exercise price.

■ At-the-Money

The exercise price is equal to the spot price of the underlying asset i.e., the current market price of the stock is equal to the exercise of strike price.

■ Out-of-the-Money

The exercise price is more than the spot price of the underlying asset i.e., the current market price of the stock is less than the exercise price.

Therefore, for a call option, the following terms are true:

If S_t > E_p, the option is in the money

If S_t < E_p, the option is out of the money

If S_t = E_p, the option is at the money

                        C₀ = Max [S_t – E_p, 0]

For put options:

If E_p > S_t, the option is in the money

If E_p < S_t, an option is out of the money

If E_p = S_t, the option is at the money

Where,

S_t is the value of the stock at expiry (time t)

E_p is the exercise price.

                        C₀ is the value of the call option at expiry

If a call option is in the money, it is exercised immediately and the option holder will earn the profit. The positive cash flow or the profit incurred to the option holder is known as the intrinsic value of the call.

Intrinsic Value

The difference between the exercise price of the option and the spot price of the underlying asset can be termed as the intrinsic value of the call.

Speculative Value

The difference between the option premium and the intrinsic value of the option can be termed as the speculative value of the call.

Example

Suppose, the exercise price of an option is Tk.200 and the market price of the share is Tk. 250. The call option is in the money. If the owner of the option exercises if he/she will make a profit equivalent of Tk. 50 (Tk.250-Tk.200). If the market price of the share is Tk. 200, the call is at the money and the holder would get no cash flow. On the other hand, if the market price of the share is less than Tk. 200, the option is out of the money and the holder would experience a negative cash flow. Thus,

The intrinsic value of a call option = S_t – E_p,        if S_t is greater than E_p

= 0         if S_t is less than or equal to E_p

The above notions indicate that the intrinsic value of a call is always greater than zero or (S_t > E_p).

One, who understands this, can become a financial engineer, tailoring the risk-return profile to meet the client’s needs. If we assume that the option expires at t, then the present value of the exercise price is:

E_p/(1 + r_f)^t

and the value of the call is:

C₀ = S₀ − E_p/(1 + r_f)^t

It is obvious from the above equation that the option value depends on the following factors:

1. The stock price: The higher the stock price, the more the call is worth and vice-versa.
2. Exercise price: The lower the exercise price, the more the call is worth and vice-versa.

iii. The time to expiration: The longer the time to expire is, the more the option is worth and vice-versa.

1. The risk-free rate: The higher the risk-free rate is, the more the call is worth and vice-versa.

Call                   Put

Stock price                                           +                           –

Exercise price                                      –                           +

Interest rate                                                +                           –

Volatility in the stock price                  +                           +

Expiration date                                                 +                          +

The value of a call option C₀ must fall within max (S₀ – E_p, 0) < C₀  < S₀.

The precise position will depend on these factors: market value, time value, and intrinsic value for an American call.

The premium of an option is the function of intrinsic value and time value. The time value of an option is the excess of the premium over the intrinsic value. Consider an example: the premium for a call option with a strike price of Tk.200 is Tk.20. If the current market price of the share underlying the call is Tk. 215, the call option is in the money. The intrinsic value of the call is Tk. 15 (Tk. 215 −Tk. 200). The premium quoted is Tk. 10, the excess of the premium over the intrinsic value Tk. 5 (Tk. 15−Tk. 10) is the time value of the call option. A call at the money or out of the money has no intrinsic value having only the time value and the entire premium represents the time value.

Let us consider a case:

Suppose the exercise price of an option is Tk. 200 with a premium of Tk. 10. If the price of the share rises above Tk. 210 (Tk. 200 + Tk. 10) at any time before the expiration date, the option holder can exercise the option to buy share at Tk. 200 and the seller is obligated to make the share available to the option holder at the exercise price (Tk. 200). Assume that the current market price of the share is Tk.250. The call option holder can make a profit by buying the share at Tk. 200 equal to Tk. 50 (Tk.250−Tk.200) with a net profit of Tk. 40 (Tk.50−Tk.10).