The Black-Scholes model was developed by Fischer Black and Myron Scholes in 1973 and later refined by Robert Merton. It was the first arbitrage free model relating the option price to the hedging strategy consisting of buying or selling the underlying asset to eliminate the risk. It is well known that some of the assumptions […]
It is crucial for quant or trading positions to have a strong understanding of the main option Greeks and how they can be used for risk management purposes. You will find below several questions you could be asked in an interview for a quant or a trading role, with possible answers. Save 25% on All […]
The option price C(S0, K, T) is homogeneous in order 1 in (S0, K) when: C(λ.S0, λ.K, T) = λ.C(S0, K, T) This is true for a large number of models such as Black-Scholes, Merton’s jump diffusion, Variance Gamma, Heston, … As detailed in the presentation below, when you differentiate both sides of the equation […]
You will find in this document the results of a series of questions posted on LinkedIn to test your knowledge on Options, Pricing and Risk Management. You will see that the good answer is not always in line with the majority of the votes! If you wish to deepen your knowledge on the pricing and […]
In previous articles (see Options, Greeks and P&L Decomposition (Part 1) and Options, Greeks and P&L Decomposition (Part 2)) we decomposed the P&L of simple option strategies in different time horizons with the major first and second order greeks. In this article, we analyse the P&L of a short iron butterfly option strategy, which is […]
In this article, we will present the Newton-Raphson method for calculating the implied volatility from option prices. Black-Scholes Price vs Volatility In Black-Scholes model, the price of an option is a function of five variables: The chart below shows the price of a European call option when changing the volatility, all other parameters being fixed. […]
The valuation and the risk management of options can be quickly complex. It depends on the option’s feature and the pricing model. There is often no closed-form solution for the pricing of the derivatives and it involves multiple dimensions. There is a vaste litterature on numerical methods such as binomial / trinomial tree, finite difference, […]
In a previous article (see Options, Greeks and P&L Decomposition (Part 1)) we analysed the decomposition of the P&L of an option strategy in a short period of time with the major first and second order greeks. In this new article, we assume that the option is kept for a certain period of time, delta-hedged […]
The Black-Scholes model is a pricing model used to determine the theoretical price of options contracts. It was developed by Fischer Black and Myron Scholes in 1973 and later refined by Robert Merton. It revolutionized the options market by providing a fair and consistent framework to calculate the fair value and to manage the risk […]
Understanding option sensitivities and greeks is crucial to be successful in trading and risk management of options. In this post we will see how to decompose the P&L of an option strategy in a short time interval with the major first and second order greeks and analyse it with several case studies. P&L Attribution and […]
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