Put-Call Parity: Replication, Synthetics, and Arbitrage Opportunities, Lecture notes of Finance

Download Put-Call Parity: Replication, Synthetics, and Arbitrage Opportunities and more Lecture notes Finance in PDF only on Docsity!

CHAPTER 10:

REPLICATION, SYNTHETICS

AND ARBITRAGE

Chapter Objectives

• This Chapter intends to introduce synthetics and arbitrage.

• On completion of this chapter you should have a good

understanding of put-call parity relationship.

• You should be able to understand the importance of why

equilibrium relationships must hold and how arbitrage is

possible when there is a disequilibrium.

Replication and Synthetics

• Two simplifying assumptions are made for these strategies:

• Interest rates and the timing difference between cash outlays now and option exercise are ignored.
• The underlying asset, exercise price and maturity of both the calls and puts are the same.

• Synthetic Long Stock Position

• Suppose 30 - day, RM 12. 00 call and put on Maybank stock are priced at RM
  1. 20 and RM 0. 15 respectively, then the strategy and payoff are as follows:
• Strategy: (to replicate long stock position) Long, RM 12. 00 , Maybank call @. 20 Short, RM 12. 00 , Maybank put @. 15

Replication and Synthetics

• Synthetic Long Stock Position

• Using call and put options, a synthetic long stock position can be created by going long a call option and shorting a put option of the same exercise price.
• Suppose 30 - day, RM 12. 00 call and put on Maybank stock are priced at RM
  1. 20 and RM 0. 15 respectively, then the strategy and payoff are as follows:
• Strategy: (to replicate long stock position) Long, RM 12. 00 , Maybank call @. 20 Short, RM 12. 00 , Maybank put @. 15
• Long Stock = Long Call + Short Put

Replication and Synthetics

• Synthetic Short Stock Position

• A synthetic short stock position can be created by going short the call and long the put option.
• Continuing with previous Maybank example, The strategy to replicate short stock position would be: Short, RM 12. 00 , Maybank call @. 20 Long, RM 12. 00 , Maybank put @. 15
• Short Stock = Long Put + Short Call

Replication and Synthetics

• Synthetic Short Stock Position

• Short Stock = Long Put + Short Call

Replication and Synthetics

• Synthetic Long Call Position

• Long Call = Long Stock + Long Put

Replication and Synthetics

• Synthetic Short Call Position

• A synthetic short call position can be established by going short a stock and an at-the-money put.
• Continuing with Maybank example, Strategy to replicate a short call position would be: Short, Maybank stock @ RM 12. 00 Short, RM 12. 00 Maybank put @. 15
• Short Call = Short Stock + Short Put

Replication and Synthetics

• Synthetic Long Put Position

• A synthetic long put position is created by going long a call option and shorting the underlying stock.
• Continuing with Maybank example, Strategy to replicate long put position: Short, Maybank stock @ RM 12. 00 Long, RM 12. 00 , Maybank call @. 20
• Long Put = Short Stock + Long Call

Replication and Synthetics

• Synthetic Long Put Position

• Long Put = Short Stock + Long Call

Replication and Synthetics

• Synthetic Short Put Position

• Short Put = Long Stock + Short Call

Replication and Synthetics

• Given the assumptions of the put-call parity, a long call and short put position have a cashflow profile that is equivalent to that of a long position in the underlying stock.

Put-Call Parity and Arbitrage

• By bringing in the interest rate, the put call parity equation is

reformed as following:

` S – K ( 1 + r ) – t^ = C + – P

• Where S = stock price (price of establishing long stock position) r = annualized interest rate K = exercise price of the options t = days to maturity of option C = call premium P = put premium
• An important implication is that any deviation from the above relationship constitutes relative mispricing and would give rise to an arbitrage opportunity. PV of exercise price

Put-Call Parity and Arbitrage

• Put-Call Parity and Arbitrage: Illustration

• Suppose, Malaysian Oxygen Bhd. (MOX) has a current stock price of RM
  11. 1. RM 10. 00 call and put options on the stock with 90 days to maturity are quoted at RM 1. 77 for the call and RM 1. 00 for the put. The annualized risk- free interest rate is 10 %.
• Mispricing is checked via using the put call parity formula S – K (1 + r ) – t^ = C + – P RM 11.00 – RM 10(1.10)–.25^ = RM 1.77 – RM 1. RM 11.00 – RM 9.76 = RM 0. RM 1.24 > RM 0.
• The put-call parity is violated. There is a mispricing differential of RM 0.47 (RM 1.24 – RM 0.77)