III. Quantitative Finance Applications

III. Quantitative Finance Applications · 14. November 2023

A swaption is a derivative allowing the choice to enter a swap, key for banks managing interest rate risks. It enables receiving a fixed rate while paying a floating rate, beneficial when hedging against rate decreases. Banks use long receiver swaptions and short payer swaptions to simulate swap payoffs in different rate scenarios. This strategy converts floating rate loans to fixed, aligning with their hedging objectives.

III. Quantitative Finance Applications · 14. November 2023

In the Black-Scholes model, N(d2) calculates the probability of a call option being in the money at expiration, balancing its potential profitability and expected exercising cost. This risk-neutral measure assumes investments grow at a risk-free rate, crucial for arbitrage-free option pricing. #BlackScholesModel #RiskNeutralValuation #OptionPricing #N(d2)Explained

III. Quantitative Finance Applications · 13. November 2023

In the Black-Scholes formula, Δ is the option delta, showing the price change of a call option for a $1 change in the stock price. Δ equals N(d1), where N is the cumulative normal distribution function, and d1 factors in the stock price, strike price, time to expiration, risk-free rate, and volatility. #OptionsTrading #Delta #BlackScholesModel

III. Quantitative Finance Applications · 11. November 2023

The Jump-to-Default Approach in option trading, modeled by an SDE, highlights how sudden stock price drops (J) affect low strike call options, especially under high credit risk. This contrasts with the Black-Scholes model, which assumes continuous price movements. In high-risk scenarios, the market often lowers the value of these options, factoring in potential defaults, and adjusts implied volatility accordingly. #OptionPricing #CreditRisk #FinancialMarkets #TradingStrategies #InvestmentRisk

III. Quantitative Finance Applications · 10. November 2023

Convertible bonds blend debt and equity, featuring an option to convert into a set number of shares. Key factors include conversion ratio and price. Valuation hinges on stock dynamics, credit risk, and hazard rate. At maturity, value is the higher of face value or conversion outcome. Monte Carlo simulations help in pricing, considering callability and putability options. #ConvertibleBonds #CreditRisk #FinancialModeling #InvestmentStrategies

III. Quantitative Finance Applications · 04. November 2023

Mean square hedging minimizes the gap between a hedging portfolio and an exotic option's payoff at maturity. It involves dynamic adjustments of holdings in risky and risk-free assets, guided by solving a stochastic differential equation and often requiring numerical methods like Monte Carlo simulations for implementation.