Derivatives option

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Currency option pricing model : 

Currency option pricing model

option mines : 

option mines A contract that grants the holder the right, but not the obligation, to buy or sell currency at a specified exchange rate during a specified period of time. For this right, a premium is paid to the broker, which will vary depending on the number of contracts purchased.

TYPES OF OPTIONS : 

TYPES OF OPTIONS Call Option :An option contract giving the owner the right (but not the obligation) to buy a specified amount of an underlying security at a specified price within a specified time. Put Option: When an individual purchases a put, they expect the underlying asset will decline in price. They would then profit by either selling the put options at a profit, or by exercising the option. If an individual writes a put contract, they are estimating the stock will not decline below the exercise price, and will not increase significantly beyond the exercise price.

EXAMPLE OF A CALL OPTION : 

EXAMPLE OF A CALL OPTION An investor buys a call option to purchase 100 IBM shares Strike price: $40 Current stock price: $38 Price of an option to buy one share = $5 Initial investment is 100 x $5 = $500 The outcome: At the expiration of the option, IBM’s stock price is $55. At this time, the option is exercised for a gain of ($55 - $40) x 100 = $1,500

Slide 5: 

When the initial cost of the option is taken into account, the net gain is $1,500 - $500 = $1,000 If the stock price is less than $40 the holder will not exercise the right to buy. In this circumstance the investor loses the whole initial investment of $500.

EXAMPLE OF A PUT OPTION : 

EXAMPLE OF A PUT OPTION An investor buys a put option to sell 100 Exxon shares Strike price: $70 Current stock price: $65 Price of an option to buy one share = $7 Initial investment is 100 x $7 = $700 The outcome: At the expiration of the option, Exxon’s stock price is $55. At this time the, the investor buys 100 Exxon shares and, under the terms of the put option, sells them for $70 per share to realize a gain of $15 per share or $1500 in total.

Slide 7: 

When the initial cost of the option is taken into account, the net gain is $1500 - $700 = $800 There’s no guarantee that the investor will make a gain. If the final stock price is above $70, the put option expires worthless and the investor loses $700.

Currency option : 

Currency option Currency options are purchased as either call options or put options. A call option gives the purchaser the right to buy a particular currency, while a put option gives the purchaser the right to sell a specified currency.

OPTIONS CAN BE EITHER : 

OPTIONS CAN BE EITHER American options: are options that can be exercised at any time up to expiration date. European options: are options that can only be exercised on the expiration date itself.

PRICING MODELS : 

PRICING MODELS A pricing model is used to find out whether the market price of a option is valid or not, so as to be able to make a decision as to buy or sell options.

Mostly used model : 

Mostly used model Black scholes model : European options The Black-Scholes is a solution to a partial differential equation binomial model : American options

Factor affecting premium charges on option : 

Factor affecting premium charges on option call/put option type American /Europe Risk free ate Volatility Time to maturity

binomial model assumption : 

binomial model assumption The binomial option pricing model assumes the rate of return on a stock can have two possible values at the end of any discrete period.  If we look at a one period model, the stock price will be either uS or dS at the end of the period.

Slide 14: 

Investor don’t want to take risk Investor would expected return is of minimum risk free rate The option pay off follows the spot price

Characteristics of binomial model : 

Characteristics of binomial model

OPTIONS CAN BE EITHER : 

OPTIONS CAN BE EITHER American European American options: are options that can be exercised at any time up to expiration date. European options: are options that can only be exercised on the expiration date itself.

limitations of binomial model : 

limitations of binomial model

Black scholes model assumption : 

Black scholes model assumption The Black-Scholes model assumes that the option can be exercised only at expiration. It requires that both the risk-free rate and the volatility of the underlying stock price remain constant over the period of analysis. The model also assumes that the underlying stock does not pay dividends; adjustments can be made to correct for such distributions. For example, the present value of estimated dividends can be deducted from the stock price in the model

Slide 19: 

Constant volatility Efficient markets No dividends Interest rates constant and known(risk-free rate) Log normally distributed returns European-style options No commissions and transaction costs Liquidity.

Slide 20: 

In their 1973 paper, The Pricing of Options and Corporate Liabilities, Fischer Black and Myron Scholes published an option valuation formula that today is known as the Black-Scholes model.

Black-Scholes Parameters : 

Black-Scholes Parameters

Black scholes formula : 

Black scholes formula d2= S = spot price

Characteristics of black scholes model : 

Characteristics of black scholes model

ONE-STEP BINOMIAL MODEL : 

ONE-STEP BINOMIAL MODEL Stock price =$22 Option price = $1 Stock price =$18 Option price = $0 Stock price =$20

Slide 25: 

t0 = ns0 –c t1=(nS0-c) (1+r) =(n Su-cu) 0r (nSd-cd) n= (cu-cd) ∕ (su-sd) u= Su /S0 d= Sd /So P=[(1+r)-d] / (u-d) c=[PCu+(1-p) Cd ] /(1+r)

Limitations of black scholes model : 

Limitations of black scholes model Constant volatility No dividends risk-free rate American-style options

Nikhil mapare : 

Nikhil mapare Thank you

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