## 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**:

** 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 strike or exercise price.

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

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

** American vs. European option:** An option can be defined as 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 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}, option is in the money

If S_{t} < E_{p}, option is out of the money

If S_{t} = E_{p}, option is at the money

* *C_{0} = Max [S_{t} – E_{p}, 0]

**For put options:**

If E_{p} > S_{t}, option is in the money

If E_{p} < S_{t}, option is out of the money

If E_{p} = S_{t}, option is at the money

Where,

S_{t} is the value of the stock at expiry (time t)

E_{p} is the exercise price.

* *C_{0} 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 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 intrinsic value of the call.

*Speculative Value*

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

Option premium = Intrinsic value + Speculative value |

**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 it 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 te 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:

C_{0} = S_{0} − E_{p}/(1 + r_{f})^{t}

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

- The stock price: The higher the stock price, the more the call is worth and vice-versa.
- 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.

- 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 *C*_{0} must fall within max (S_{0} – E_{p}*,* 0) __<__ C_{0} __<__ *S*_{0}.

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 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 being 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).

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