III. Quantitative Finance Applications

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.
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
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
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
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
The Put-Call Symmetry (PCS) in Layman’s terms… 
Put-Call Symmetry (PCS) links European put and call option prices via the forward price of the underlying asset. It requires frictionless markets, no arbitrage, zero drift, and symmetric asset returns. PCS is practical for pricing and hedging exotic options, offering a simpler alternative to dynamic hedging by balancing put and call strike prices against the forward price.

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.
Cointegration in Layman’s Terms…
Explore cointegration in finance with our easy guide. Learn pairs trading & hedging with assets that move together long-term, offsetting risks. Master the Engle-Granger method & visualize asset correlation for informed investment. Updated, mobile-optimized content for every investor. #Cointegration #TradingStrategy

Why delta is not the probability of an option expiring in the money in layman’s terms…
Unpack the myth that option Delta equals the probability of expiring in-the-money. Dive into risk-neutral valuation and the Black-Scholes model, where assets grow at a risk-free rate, making Delta an unreliable real-world probability indicator. Explore the distinction for smarter option trading. #OptionTrading #BlackScholes #RiskNeutralValuation

Gamma Neutrality in layman’s terms…
Explore the connection between Tesla's advanced speed regulator and the concept of gamma neutrality in options trading. While delta signifies the speed (akin to an option's price movement relative to its asset), gamma represents acceleration, indicating how delta evolves. Achieving gamma neutrality in trading parallels maintaining both speed and acceleration in a Tesla, ensuring a predictable and smooth drive.

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Contact: Florian CAMPUZAN Phone: 0680319332 Email:fcampuzan@finance-tutoring.fr 

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