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DERIVATIVES & RISK MANAGEMENT

Name:Mohmedfaizal Kadri Roll

No.:302422

Assignment:01 (Put call parity) Date:

24thJuly, 2013

INTRODUCTION :

This assignment is about a conceptual understanding of the Put call parity. It refers to

the relationship between call and put options for a provided stocks, strike price and date of

expiry. Under put-call parity, the optionprices should match, yielding noprofit no loss or say

euilibrium.

Put call parity is an attractive, noticeable opportunity arising from the options markets.

!y clear understanding of put call parity, one can begin to better understand the procedure thatprofessional investors may use to value options, how demand and supply impacts option prices

and how all option values "at all the strike prices available and expiry date# related on the same

underlying security.

UNDERSTANDING THE PUT-CALL PARITY :

To understand how the put call parity can be work, we should first know these points.

$# Put call parity applicable only when one or % both are &

a. 'uropean (ption.

b. !oth portfolios expire on the same day and,

c. !oth have same strike price.

)# *orkout the argument consider two Portfolio + and !.

# Portfolio + consists of an 'uropean call option and cash eual to the number of shares

covered by the call option multiplied by the strike price. Portfolio ! consist of an

'uropean put option and the underlying asset.

http://www.investinganswers.com/financial-dictionary/optionsderivatives/option-2049http://www.investinganswers.com/financial-dictionary/businesses-corporations/profit-2042http://www.investinganswers.com/financial-dictionary/businesses-corporations/profit-2042http://www.investinganswers.com/financial-dictionary/optionsderivatives/option-2049

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# or St > k&P"+# / 0t 1 'xercise the call option by paying money k by share "0t#2 and

P"!# / 0t 1 3o not exercise the put option share is at value 0t2

Therefore, P"+# / P"!#

4# or St < k&

Inserting the 5alue of portfolio C +KerT= P + Soand therefore

K = (P + So C) erT

The equation suggests that knowing the price of one option the price of the other option

calculated because K and So are known.

+. k< (P + So C) erT:

a# *rite a Put option "6p#

b# 0ell a share short "60o#

c# !uy a 7all "-7#

IfSt > k= o not e!ercise the Put option.

If St < k= we will e!ercise the Put option and do not e!ercise the call option.

"e will recei#e (P + So C) $er% from the bank.Put option will exercised. %herefore bu& the share b& pa&ing a'ount K.

0ettle the short with a share purchased in 0tep ).

Profit / "P + So C)

$e

r%- %

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!. k> (P + So C) erT:

a# !orrow " P 6 0o+ C)

b# u& a Put option

c# !uy a share

d# *rite a call.

IfSt > k= "e will sell a share and recei#e K.

IfSt < k= %hen again K (P + So C) $er%

Therefore, % must be / (P + So C) $er%

Note :eferring the P(*) = P() therefore K = (P + So C) $er% for % 8 (P + So C) $er% arbitragesituation will prevail. Under this circumstances ollowing steps will take &

0ituation + &

0t 8 k, Put option 9apse, 7all option exercised. 0o give share and get %.

(ut of % return "P + So C) $er%

Therefore Profit / % - (P + So C) $er%

0ituation ! &

7onsider 0t : k, Put option will exercised. 3eliver the share which we have already

purchased.

UPPER BOUND & LOWER BOUND :

1) Uppe Bo!"# :

+n 'uropean call option gives a right to the buyer to purchase a share at a certain price.The call option cannot be more than the stock price.

c S0

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)# Lo$e Bo!"#:

The lower bound in the 'uropean put options will be &

p KerT S0

PROBLE% :

0tock price / ;s. # / >).