Pricing of Derivatives

8/12/2019 Pricing of Derivatives

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PRICINGOFDERIVATIVES


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GROUPMEMBERS:

Arzan Irani M4221

Amruta Chavan M4210

Rishikesh Surve M4252

Sandesh Sawal M4247

Tejal Rashivate M4245


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FACTORSAFFECTINGOPTIONPRICES:

The current stock price, So

The strike price, K

The time to expiration, T

The volatility of the stock price,

The risk-free interest rate, r

The dividends expected during the life of the option.


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WHATISSTOCKPRICE& STRIKEPRICE??

For call options, the strike price is where the security can be

bought(up to the expiration date). For put options, the strike price is the price at which shares

can be sold.


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STOCKPRICE& STRIKEPRICE:

For a call option, the payoff will be the amount by which the

stock price exceeds the strike price.

Call options therefore become morevaluable as the stock

price increases and lessvaluable as the strike price

increases.

For a put option, the payoff on exercise is the amount by

which the strike price exceeds the stock price.

Put options therefore behave in the opposite way from call

options.

They become lessvaluable as the stock price increases and

morevaluable as the strike price increases.


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MONEYNESS In the money:An in-the-money (ITM) option has positive

intrinsic value as well as time value.Call option strike price < spot price

Put option strike price > spot price

At the money: An at-the-money (ATM) option has no intrinsic

value, only time value.

Call & Put option strike price = spot price

Out of the money:An out-of-the-money (OTM) option has no

intrinsic value.Call option strike price > spot price

Put option strike price < spot price


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TIMETOEXPIRATION A specified time after which the option contract is no longer

valid is known as time to expiration.

Expiration of an option contract is the last date on which the

holder of the option may exercise it according to its terms.

The last day to trade an option is the last Thursday of the

expiration month and if that Thursday is trading holiday then it

would be the previous day. European options cannot be exercised before the expiry of the

contract.

American options can be exercised before the expiry of the

contract.

European options may or may not become more valuable asthe time to expiration increases

American options become more valuable as the time to

expiration increases.


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EXAMPLE: Consider 2 European call options on a stock:

One with an expiration date in 1 month & the other with anexpiration date in 2 months.

Suppose that a very large dividend is expected in 6 weeks.

The dividend will cause the stock price to decline, so that the

short-life option could be worth more than the long-life option.


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VOLATILITY The owner of a call benefits from price increases but has

limited downside risk in the event of price decrease because

the most the owner can lose is the price of the option

(premium).

Similarly, the owner of a put benefits from price decreases, but

has limited downside risk in the event of price increases.

The values of both calls and puts therefore increases asvolatility increases.


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INTRINSICVALUE The intrinsic value (or "monetary value") of an option is its

value assuming it were exercised immediately.

Thus if the spot price of the underlying security (or commodity

etc.) is above the strike price, a call has positive intrinsic value

(and is called "in the money"), while a put has zero intrinsic

value (and is "out of the money").


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TIMEVALUE The time value of an option is the total value of the option,

less the intrinsic value.

It partly arises from the uncertainty of future price movements

of the underlying.

A component of the time value also arises from the unwinding

of the discount rate between now and the expiry date.

In the case of a European option, the option cannot beexercised before the expiry date, so it is possible for the time

value to be negative;

For an American option, if the time value is ever negative, you

exercise it.


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Underlying

price (Rs.)

Strike Price

(Rs.)

Premium

(Rs.)

Intrinsic

Value (Rs.)

Time Value

(Rs.)

100 90 12 10 2

101 90 13 11 2

103 90 14 13 1

88 90 1 0 1

95 90 5.50 5 0.50

INTRINSIC AND TIME VALUE FOR CALL OPTION

EXAMPLE


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Underlying

price (Rs.)

Strike Price

(Rs.)

Premium

(Rs.)

Intrinsic

Value (Rs.)

Time Value

(Rs.)

100 110 12 10 2

99 110 13 11 2

97 110 14 13 1

112 110 1 0 1

105 110 5.50 5 0.50

INTRINSIC AND TIME VALUE FOR PUT OPTION

EXAMPLE


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BLACK SCHOLES MODEL

Pricing of Derivatives

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