Hedging and rebalancing portfolio in a binomial tree
Hedging and rebalancing portfolio in a binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Table of Contents: • • Options Binomial Trees Hedging Using Python Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Options: • • • Basic terms - strike price - expiration date Call options - right to buy Put options - right to sell Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree American options - exercised any time before or at the expiration date • European options - only be exercised at the expiration date • Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree • Changes in the option price due to the increasing value of one variable: Variable European call European put American call American put Current stock price + - Strike price - + Time to expiration ? ? + + Volatility + + Risk-free rate + - - + Amount of future dividends (+) indicates that an increase in the variable causes the option to increase (-) indicates that an increase in the variable causes the option price to decrease (? ) indicates that the relationship is uncertain Source: John C. Hull, 2008 Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree • The Greeks - Δ: rate of change on the price of the option with respect to the price of the underlying asset - Θ: rate of change of the value with respect to time - Γ: rate of change of the portfolio‘s delta with respect to the price of the underlying asset - ν: rate of change of the value of the portfolio with respect to the volatility - ρ: rate of change of the value of the porfolio with respect to the interest rate Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Binomial Trees • • represents the different paths of a stock value in each step there is a certain probability of moving up or down u. S, Φ(u) S 0 d. S, Φ(d) Figure 1 Representation of one step binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Hedging • Investment position to eliminate any losses or gains • Wide range of financial instruments - Stocks - Derivatives - Swaps - Future contracts • Greeks = 0 • Delta hedging • Delta- Gamma hedging Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree • Conclusion • • European and American Options The Greeks Delta and Delta- Gamma Hedging The binomal model in the programming language python Andromachi Boulougari - Pablo Matute - Belinda Strass 2016/10/19
Hedging and rebalancing options in a binomial tree Thank you for your attention Andromachi Boulougari – Pablo Matute – Belinda Strass
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