Executive stock options usually have complex payoffs. To price them, we often use the binomial tree method or Monte Carlo simulations. … a lattice model can be designed to accommodate dynamic assumptions of expected volatility and dividends over the option’s contractual term, and estimates of expected option exercise patterns during …

In a previous post, we presented a method for pricing a fixed-rate bond. In this post, we are going to discuss valuation of a callable bond. A callable bond (also called redeemable bond) is a type of bond (debt security) that allows the issuer of the bond to retain the …

A warrant is a financial derivative instrument that is similar to a regular stock option except that when it is exercised, the company will issue more stocks and sell them to the warrant holder. Warrants and options are similar in that the two contractual financial instruments allow the holder special …

In a previous post, we wrote about Employee Stock Options, a form of financial compensation that a company uses to reward its employees. In this post, we are going to discuss another form of compensation, Performance Share Units. Performance share units (PSUs) are hypothetical share units that are granted to …

Employee Stock Option (ESO) is a form of compensation that a company uses to reward, motivate, and retain its employees. An employee stock option (ESO) is a label that refers to compensation contracts between an employer and an employee that carries some characteristics of financial options. Employee stock options are …

In a previous post, we presented the binomial tree method for pricing American options. Recall that an American option is an option that can be exercised any time before maturity. A drawback of the binomial tree method is that the implementation of a more complex option payoff is difficult, especially …

Just like any financial derivatives that were initially designed for risk management purposes, interest rate swaps are an effective tool for managing and transferring interest rate risks as long as those risks are well understood.  But as banks and financial institutions are constantly trying to invent new financial products to …

In a previous post, we presented a methodology for pricing European options using a closed-form formula. In this installment, we price these options using a numerical method. Specifically, we will use Monte Carlo simulation. Recall that, A call option gives the buyer the right, but not the obligation to buy …

The Black-Scholes-Merton model is one of the earliest option pricing models that was developed in the late 1960s and published in 1973 . The most important concept behind the model is the dynamic hedging of an option portfolio in order to eliminate the market risk. First, a delta-neutral portfolio is …

A derivative is a financial instrument whose price is derived from one or more underlying assets. Thus, in very simple words, the price and value of a derivative stem from its underlying assets. The underlying assets can be anything that have some value. In the first part of this article, …