# Replication vs Hedging

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FINS3635 S1/2012

Replication vs. Hedging

Matthias Thul∗

Last Update: March 31, 2012

The document “Replication of Forward Contracts” discusses how we can price forward

contract by replicating their terminal payoﬀs and then employing a no-arbitrage argument to

obtain the fair forward price. While replication is based on constructing a portfolio who’s

terminal cash-ﬂows match those of the forward contract, we can equivalently price the forward

contract by constructing a hedging portfolio. This is a portfolio chosen such that all cash-ﬂows

after the initial point in time are zero. We can then again infer the fair forward price by a

no-arbitrage argument. These two approaches are closely linked and the positions taken in

these approaches have opposite signs.

Underlying Asset without Holding Returns

We ﬁrst assume that the underlying asset has no holding returns. We combine positions in the

underlying asset with lending or borrowing transactions such that we oﬀset all cash-ﬂows after

the initial date. The steps that we need to take are:

(i) Oﬀset the uncertain Component:

The payoﬀ of a long (short) position in the forward contract consists of two components, a

ﬁxed cash-ﬂow of −F0 (+F0 ) and a variable cash-ﬂow of +ST (−ST ). The latter depends

upon the price of the underlying asset at t = T which is uncertain as of t = 0. We thus

start by entering a transaction in the underlying asset such that the uncertain component

of the forward contract’s payoﬀ is oﬀset.

In case of a long position in one unit of the forward contract, we need to sell one stock.

This position has value of −ST in t = T and exactly oﬀsets the +ST term in the forward

contract’s payoﬀ. We obtain:

The author can be contacted via #first letter of first name#.#last name#@unsw.edu.au and

http://www.matthiasthul.com.

1

instrument

position

cash-ﬂow

t=0

t=T

forward

+1

0

ST − F0

underlying asset

−1

+S0

−ST

(ii) Oﬀset all Cash-Flows...