What is Volatility Smile? The expression “volatility smile” refers to the variation in implied volatilities of options based on their strikes. A smile indicates that out-of-the-money puts and calls have…
What is Complete Market and Incomplete Market? In a complete market, derivative products can be created by combining basic instruments like cash and underlying assets. Typically, a portfolio of simpler…
How Jump Diffusion Model works? In jump diffusion model, prices are permitted to jump discontinuously in addition to the continuous Brownian motion (the diffusion) observed in Black-Scholes models. Typically, the…
What is the finite difference method? The finite difference method converts continuous differential equations into discrete differential equations, allowing for numerical solutions. This approach is particularly beneficial for problems with…
Which Numerical Methods Should be Used? The three most common numerical methods are Monte Carlo, Finite difference, and Numerical Quadrature. (I include the binomial approach as a simplified version of…
What is Monte Carlo Simulation? Monte Carlo Simulation is a method of solving probabilistic problems that involves numerically ‘seeing’ many alternative scenarios or games in order to quantify statistical attributes…
What are Forward and Backward Equations? Forward and backward equations are differential equations that govern the transition probability density function of a stochastic process. Diffusion equations must be solved in…
What is Volatility? Volatility refers to how much an investment’s price fluctuates over time. It’s similar to a mood swing meter: high volatility denotes wild ups and downs, whilst low…
Why Do Quants like Closed-Form Solutions? Because quants are quick to compute and simple to grasp. A Short Example The Black-Scholes formulas, despite their shortcomings, are frequently used to unintended…
What is Greek Terminology in Finance? The Greek Terminology or simply the ‘greeks’ refer to the price sensitivity of derivatives to various underlyings, factors, and parameters. Differentiating option values with…
The Whispering Void