Tag: Options

Effect of Interest Rate and Volatility

Effect of Interest Rate and Volatility

In CFA Fixed Income curriculum, module 3, section 3, "Effect of Interest Rate Volatility", the impact of interest rate volatility on the value of callable and putable bonds is explored. In this blog post, I will replicate the examples from the CFA curriculum using Python code, leveraging the QuantLib library for bond valuations, including: Effect … Continue reading Effect of Interest Rate and Volatility

Pricing Callable and Putable Bonds with QuantLib

Pricing Callable and Putable Bonds with QuantLib

The valuation and analysis of bonds with embedded options is the most focused topic discussed in the CFA Level 2 Fixed Income curriculum. These types of bonds, such as callable and puttable bonds, introduce an additional layer of complexity due to the optionality features embedded within the instrument. In this blog post, I will discuss … Continue reading Pricing Callable and Putable Bonds with QuantLib

Implied Volatility Calculation

Implied Volatility Calculation

Implied volatility (IV) is a key metric in options trading and risk management. It is derived from the market price of an option and reflects the market's consensus view on the expected future volatility of the underlying asset. There is a lot of information that can be interpreted from IV. For example, high IV often … Continue reading Implied Volatility Calculation

Dynamic Delta Hedging with DolphinDB

Dynamic Delta Hedging with DolphinDB

Delta hedging is an options trading strategy used to maintain a delta neutral position by ensuring that the overall delta of a portfolio is zero, so that the price fluctuations of the underlying asset do not significantly impact the position’s value. Dynamic delta hedging involves continuously adjusting the hedging position to account for changes in … Continue reading Dynamic Delta Hedging with DolphinDB

Real-Time Option Greeks Calculation with DolphinDB

Real-Time Option Greeks Calculation with DolphinDB

In the previous blog post, we explored option Greeks calculations using the BSM model. In this post, I’ll have some coding fun by implementing real-time Greeks calculations with the formulas from the last post, but this time using the DolphinDB stream processing framework. Here, I plan to mimic a portfolio consisting of option contracts with … Continue reading Real-Time Option Greeks Calculation with DolphinDB

Options Greeks

Options Greeks

Options Greeks are key metrics used in options trading and risk management to measure how sensitive an option's price is a series of factors, including: Delta - measures the sensitivity of an option's price to the changes in the underlying asset's price. Gamma - measures the change rate of an option's Delta in respect to … Continue reading Options Greeks

Swaption Valuation

Swaption Valuation

A swaption is an option on an interest rate swap. As previously discussed, an interest rate swap involves two parties: the fixed-rate payer (who receives the floating rate) and the fixed-rate receiver (who pays the floating rate). A swaption grants the holder the right, but not the obligation, to enter into a swap contract as … Continue reading Swaption Valuation

Interest Rate Options Valuation

Interest Rate Options Valuation

Interest rate options are options based on interest rates, where the underlying asset is a reference interest rate, typically in the form of a Forward Rate Agreement (FRA). For instance, an interest rate call option on a 3-month MRR (market reference rate) with 9 months to expiration would have a 3-month FRA rate expiring in … Continue reading Interest Rate Options Valuation

Futures Options Pricing with Black Model

Futures Options Pricing with Black Model

In the last blog post, we explored the Black-Scholes-Merton model and learned that it is the industry standard for pricing option contracts. However, the BSM model is designed for options on stocks and similar spot market assets, and it is not directly applicable for pricing futures options contracts, mainly due to the following differences between … Continue reading Futures Options Pricing with Black Model

Black-Scholes-Merton (BSM) Model

Black-Scholes-Merton (BSM) Model

In the previous blog post, we saw that the binomial model closely approximates option prices as the number of periods increases. The binomial model is known for its flexibility, intuitiveness, and fewer assumptions. So, why do we still need the Black-Scholes-Merton (BSM) model for option pricing, especially given its restrictive assumptions? One of the main … Continue reading Black-Scholes-Merton (BSM) Model