Derivatives

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Derivatives and Risk Management

Assignment 1 1st Oct 00

Example 1.5

The example given in section 1.7 of the text book is a Range or Flexible Forward. The meaning of this clearly comes out in the example. The person who buys this forward has only two prices to pay, known as the upper band and the lower band, depending upon whether the then spot price is greater or lower than the band respectively. If the price is in between the bands, the person pays actual spot rate applicable then.

Clearly this is a combination of two options

1) One is to Buy a call option at the higher price also known as upper band

) And another is to Sell a put option at the lower price known as lower band

The premium should be same in both the cases.

Let us see the example between US Dollar ($) and Pound Sterling (£)

Spot Price Put Option

@ 1.400 Call Option

@ 1.4600 Comments

SP =1.400 Exercised Expires buy at 1.400

1.400SP1.4600 Expires Expires Market Rate

SP =1.4600 Expires Exercised buy at 1.4600

This is called a forward contract because if the band width is zero, its value becomes zero and functions as a simple forward contract.

Example 1.1 (Using DerivaGem)

Given values are put into the s/w as given. Exchange rate volatility=15% p.a., Dollar risk-free rate = 5% p.a., Sterling risk-free rate = 6.4% p.a., time=0.5 years, Exercise Price = 1.4.

Then, (DerivaGem gives)

Value of the Put option = 0.048555.

Value of the Call Option = 0.01854. Since, these two values are not matching, we adjust the upper end of the band so that the contract has zero value initially.

After doing that we get the new upper band at 1.455 instead of 1.4600

Thus, when we adjust the upper band of 1.4600 to arrive at the value equal to the put option, we get the required upper band is 1.455.

Example 1.

Consider both the scenarios faced by the trader

The gold dealer first borrows gold for $50 at the given 6% p.a. The amount he has to pay after a year become $50+ 6%50$ = $65

The gold dealer next sells gold for $4 and invests the same amount at 5.5% p.a. After a year he is expected to get back $4+$505.5% = $6.65

Hence, for no arbitrage has to take place in the market, the price has to be in between $65 and $6.65.

Niranjan Reddy Renati, 7, Sec B

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