DERIVATIVES

An option is a contract that provides its holder with the right to buy or sell an underlying asset or security. It involves a specific price before or on a predetermined date. However, it does not obligate them to do so. There are several option styles, which represent the class into which an option falls.…

Read More Bermudan Option: Definition, Example, Pricing

Convertible bonds are complex securities that are part debt, part equity. The main feature of a convertible bond is the conversion that allows the bondholder to convert debt to equity. In addition, there can be many other “exotic” features such as callable, puttable, forced conversion, soft call, contingent conversion, etc. Given their complexities, convertible bonds’…

Read More Pricing Convertible Bonds Using Monte-Carlo Simulations

We previously discussed implied dividend yield and how to extract it from traded financial instruments. Given that dividend is considered a cash payment the shareholder receives when holding a stock, naturally one would think that dividend yield can only be zero or positive. We recently, however,  worked with a client whose implied dividend yield is…

Read More Can Dividend Yield Be Negative?

Black-Scholes-Merton (BSM) is a celebrated option pricing model that is used frequently in the financial industry [1]. The model was developed initially for equity options but then has been extended to many asset classes. It is so frequently used, to the point that the practitioners almost do not pay attention to the underlying assumptions of…

Read More Valuation of European Options with Stochastic Interest Rates and Transaction Costs

Derivatives are financial products whose values are determined by the current price of the underlying asset or portfolio. Weather derivatives are a particular class of financial instruments that individuals or companies can use in support of risk management in relation to unpredictable or adverse weather conditions. While some may see them as an exciting innovation,…

Read More Pricing of Weather Derivatives Using Monte Carlo Simulations

Dividend yield is an input into the option valuation model that often receives little attention from practitioners. This is probably because the majority of companies do not pay dividends. And for those that pay, an inaccuracy in the estimation of the dividend yield often has a small impact on the fair value of the financial…

Read More How to Determine Implied Dividend Yield-Derivative Valuation in Excel

The Binomial tree is a standard method for pricing American style options. Recall that, The Binomial options pricing model approach has been widely used since it is able to handle a variety of conditions for which other models cannot easily be applied. This is largely because the BOPM is based on the description of an…

Read More The Willow Tree Method, an Advanced Option Pricing Model

Convertible bonds are complex, hybrid securities. In finance, a convertible bond or convertible note or convertible debt (or a convertible debenture if it has a maturity of greater than 10 years) is a type of bond that the holder can convert into a specified number of shares of common stock in the issuing company or…

Read More Convertible Bond Arbitrage Using the Volatility Surface

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 the option’s contractual term, including…

Read More Valuation of Executive Stock Options Using a Closed-Form Formula

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 privilege of redeeming the bond…

Read More Valuation of Callable Putable Bonds-Derivative Pricing in Python