Chasing Swallowtail butteflies Last weekend in Nathiagali late in the afternoon, while lazing around on a sun deck chair, I noticed that the butterflies around our bunglow were feasting on a single flower laden tree. Baba and I had finally sat down to chat and I had been telling him about how the the most recent [...]
Implied volatility and relative hedging P&L. Four scenarios to set things right. We go back to a simple world where implied volatility can take four possible values. 10%, 20%, 30% and 40%. As a trading desk we can write and sell options at each of these implied volatility levels. We decide to write a call option. [...]
Review Option Greeks Primer – Sign up deadline this weekend Option Greeks Primer will be published by Palgrave Macmillan in Q3 of 2014. The book is aimed at bridging the gap that exists in Greeks coverage in academic and practitioner literature. Twenty years ago when I went looking for material on convexity most books on Fixed Income Portfolio [...]
What makes a book? There is so much more that goes in shipping a book to the publisher than just writing it. Two days ago when I shipped the final manuscript to my editorial team, it felt like a time to celebrate and we did. A private sushi dinner and the Edge of Tomorrow provided welcome relief [...]
Vega, Volga and Vanna. The volatility Greeks. What is Vega? Vega is the change in the value of the option with respect to change in volatility. Within the Greeks Vega’s importance rises given how misunderstood the behaviour of volatility is and the impact changes in volatility have on option prices. In earlier chapters we have seen: a) [...]
Gamma correction & Delta hedging P&L results. A simple case study Theoretically speaking in the Black Scholes world the cost of the hedge should be close to the theoretical value of the option. In our cash accounting P&L we have included the theoretical premium received which is used in determining the initial amount to be borrowed. [...]
Calculating Shadow Gamma (Option Greeks) We use a simple example to illustrate the calculation of Shadow Gamma as describe by Taleb in Dynamic Hedging. Gamma is the second derivative of the change in option price to a change in the underlying asset price. Alternatively, it is the rate of change in the option delta to a change [...]
Building an illustrative Vega and Gamma hedging model in Excel. We build a simple Excel spreadsheet that allows us to hedge Gamma and Vega exposure for a single short position in a call option contract. Gamma and Vega hedges are created by buying cheaper out of money options with shorter or similar maturities. The five lessons [...]
Hedging portfolio Vega and Gamma using solver. Lesson Five For our portfolio model we need an objective function that allows us to minimize the cumulative Greek gap across maturity buckets with respect to Vega and Gamma between the short positions and the proposed hedge portfolio. We will try two alternates. In the first instance we calculate cumulative [...]
Lesson Four – Hedging higher order Greeks for a book of short call options We are now ready to move to a more sophisticated version of our hedging higher order Greeks problem. Rather than limiting ourselves to a single short position we are going to go ahead and sell multiple options. Here is an inventory of [...]