INTRODUCTION A portfolio is said to be a mimicking portfolio if it produces the same profit as another portfolio, but does not incur the same entry fee at inception or the same payoff at

Put-Call Parity

or

INTRODUCTION

1. A portfolio is said to be a mimicking portfolio if it produces the same profit as another portfolio, but does not incur the same entry fee at inception or the same payoff at expiration.
2. A portfolio is said to be a synthetic portfolio if it produces the same profits as another portfolio AND has the same entry fee and same payoff at expiration.
3. A hedge is a security that produces similar cash flows to your current investment and is normally sold short so that it produces gains when the current investment incurs losses, or produces losses when the current investment produces gains. For example, an investor who owns ABC stock can perfectly hedge his position by selling short DEF stock if ABC and DEF are expected to rise and fall together. In this way, if the market goes down, then ABC’s losses are offset by DEF’s gains. Similarly, if the market goes up, then ABC’s gains are offset by DEF’s losses.

SYNTHETIC PORTFOLIOS

We can demonstrate that a portfolio is a synthetic portfolio in two ways:

Method #1: we can show that:

a. the entry fee for A is the same as the entry fee for B

b. the profit for A is the same as the profit for B

Alternatively, Method #2: we can show that:

a. if we enter into portfolio A (i.e. incur the entry fee) and hedge by selling portfolio B (i.e. receive the entry fee, rather than pay the entry fee) then we have a net expense of zero at inception.

b. at expiration any profit (or loss) earned on A will be offset by any loss (or profit) on B with a net gain of zero at expiration.

ARBITRAGE

If Portfolio A’s entry fee is not equal to Portfolio B’s entry fee, then an investor can make a riskless profit using method #2 above.

To take advantage of an arbitrage situation, one would simply lock in the profit by:

1. buying the cheaper portfolio (i.e., paying the lowest entry fee) and simultaneously
2. selling the expensive portfolio (i.e., receiving the highest entry fee).

PRACTICE EXAMPLES _________________________________________________

Consider the following information on put and call options on a stock:

Call price, C₀ = $4.50

Put price, P₀ = $6.80

Exercise price, X = $70

Days to expiration = 139

Current stock price, S₀ = $67.32

Risk free rate, r = 5%

1) Use put-call parity to calculate the prices of the following:

A. Synthetic call option

B. Synthetic put option

C. Synthetic bond

D. Synthetic underlying stock

2) For each of the synthetic instruments in (1), identify any mispricing by comparing the actual price with the synthetic price.

3) Based on any mispricing in (2), illustrate an arbitrage transaction to exploit the mispricing.

Дата добавления: 2015-11-04