Aaron Bany May 21, 2013 BA Financial Markets and Institutions

What is an option?  A financial derivative that represents a contract sold by one party (writer) to another party (holder)  It offers the holder the right, but not the obligation, to exercise the option to either buy or sell an underlying asset when predetermined conditions are met

How Options Function Option = f(S, K, T, r f, σ) S = share price K = strike price T = time to maturity r f = risk free rate σ = volatility of underlying asset

2 Types of Options  Vanilla Options (2 forms) American Option European Option  Exotic Options (unlimited) Bermuda Options Chooser Options Performance Options Compound Options Binary Options Barrier Options Asian Options Lookback Options Etc.

Exotic Options  The term “exotic” was popularized by Mark Rubinstein in 1990  Used to describe any option that is more complex than a vanilla American or European option

Binary Options  It either pays out or it doesn’t  2 types Cash-or-Nothing ○ Pays the fixed amount if the asset is “in-the- money” Asset-or-Nothing ○ Pays the value of the underlying

Barrier Options: Knock-In  Up-and-in: activated by moving up and beyond the barrier  Down-and-in: activated by moving down and beyond the barrier  Knock-In Call option – Asset begins the day at $75 Scenario 1 Time = 1 day Strike Price = $80 Barrier Price = $90 Closing Price = $85 Call Payout = $0 Scenario 2 Time = 1 day Strike Price = $80 Barrier Price = $90 Closing Price = $95 Call Payout = $15

Barrier Options: Knock-Out  Up-and-out: deactivated by moving up and beyond the barrier  Down-and-out: deactivated by moving down and beyond the barrier  Knock-Out Call option – Asset begins the day at $75 Scenario 3 Time = 1 day Strike Price = $80 Barrier Price = $90 Closing Price = $85 Call Payout = $5 Scenario 4 Time = 1 day Strike Price = $80 Barrier Price = $90 Closing Price = $95 Call Payout = $0

Barrier Options Double One-Touch Double No-Touch One-Touch No-Touch

Why Binary and Barrier Options?  You don’t have to be an expert trader  You know the risk and payoff  Short time to maturity  High payout ROI of 50-70% Linked to the direction the asset trending and not the difference in price

Asian Options  Originated in Tokyo, Japan in 1987  Payoff is based on the average price of the asset over a pre-set period of time  Fixed Strike – payoff is the difference between the strike price and average value  Floating Strike – payoff is the difference between value at expiration and average value

Asian Option Example Fixed StrikeFloating Strike Average = $102 Pre-Set Strike = $80 Call Payout = $22 Put Payout = $0 Average = $102 maturity = $110 Call Payout = $0 Put Payout = $8

Why Asian Options?  Reduce the dependence of the value of the option on the spot price of the asset on a specific date  Less expensive because its volatility is usually less then the underlying assets spot price

Lookback Options  Payout depends on the underlying assets maximum (call) or minimum (put) price over the life of the option  Fixed Strike – payoff is the difference between a pre-set strike and the min or max value  Floating Strike – payoff is the difference between optimal price (the strike) and the min or max value

Lookback Options Fixed StrikeFloating Strike Pre-Set Strike = $95 Highest Price = $130 Call Payout = $35 Lowest Price = $75 Put Payout = $20 Highest Price = $130 Lowest Price = $75 Call Payout = $55 Put Payout = $55

Why Lookback Options?  It eliminates the market entry and exit problems  Completely maximizes profit

Mini Quiz: Q1 The current price of a stock is trading at $2.50. The trader believes that the stock has high volatility and could rise above $2.55 or drop below $2.45. What is the best option to capitalize on this scenario? A.Asian Option B.Lookback Option C.Binary Option D.Double One-Touch Option Double One-Touch

Mini Quiz: Q2 A trader buys a European call option with X = $100, that is trading at $100. The asset falls to $70 before rallying to $120. The trader decides to hold it to see if it will rally higher, but it falls to $80 at maturity. What option gives the highest payout? A.Asian Option B.Lookback Option C.Binary Option D.Double One-Touch Option

Questions

Sources      Bermin, H., Buchen, P., & Konstandatos, O. (2008). Two Exotic Lookback Options. Applied Mathematical Finance, 15(4), doi: /