Option Pricing

Accumulator Option Pricing

May 29, 2019
Option Pricing

An accumulator is a financial derivative that is sometimes known as “I kill you later". This post attempts to explain how it is structured and price it via Monte Carlo simulations in Python. 1. Overview of Accumulator Like all derivatives, there are two parties invovled in an accumulator, the buyer and the seller, both agree on a strike price that is usually at a discount to the prevailing market price of the underlying security at the time of contract origination. ...

Call Option Value from Two Approaches

Mar 17, 2019
Option Pricing

Suppose today the stock price is $S$ and in one year time, the stock price could be either $S_1$ or $S_2$. You hold an European call option on this stock with an exercise price of $X=S$, where $S_1<X<S_2$ for simplicity. So you’ll exercise the call when the stock price turns out to be $S_2$ and leave it unexercised if $S_1$. 1. Replicating Portfolio Approach Case 1 Case 2 Stock Price $S_1$ $S_2$ Option: 1 Call of cost $c$ Exercise? ...

Reconciliation of Black-Scholes Variants

Apr 17, 2018
Option Pricing, Black-Scholes

This post is just to show that the different variants of Black-Scholes formula are in fact the same. $S$: Underlying share price $t$: Time to maturity $\sigma$: Standard deviation of underlying share price $K$: Exercise price $r_f$: Risk-free rate Variant 1 This is the one shown in our formula sheet, and is also the traditional presentation of Black-Scholes model. $$ \begin{equation} C=SN(d_1)-N(d_2)Ke^{-r_f t} \end{equation} $$ $$ \begin{equation} d_1=\frac{ln(\frac{S}{K})+(r_f+\frac{\sigma^2}{2})t}{\sigma \sqrt{t}} \end{equation} $$ ...