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- I. Stochastic Models and Processes
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VIII. Quant Interview Questions · 14. November 2023

To find the probability that the barrier is breached at any time between now and a future time T, we can use the reflection principle of Brownian motion. However, without going into complex stochastic calculus, a simplified approach can consider the probability that the stock price exceeds H at time T. This probability can be expressed using the cumulative distribution function (CDF) of the normal distribution, denoted as Phi. The stock price at time T is normally distributed with mean equal to...

VIII. Quant Interview Questions · 14. November 2023

Quant Interview Question: European Call Option Pricing with Different Volatility Assumptions You're tasked with pricing a European call option under two different scenarios: 1. Using a constant volatility of 20%. 2. Drawing volatility from a random distribution with an average of 20%. ________ Which option do you anticipate would generally be more expensive, and why? At a first glance, many would assume that the option with stochastic volatility would come with a heftier price tag. This is...

VIII. Quant Interview Questions · 14. November 2023

Which of the following statements about Volga is most accurate? A. Volga is the rate at which vega changes with respect to the underlying price B. High Volga values imply that options are more sensitive to kurtosis risk of the underlying asset C. Volga becomes particularly important when trading binary options due to their vega profile D. All else being equal, an option with a longer time to maturity will always have a higher Volga than an option with a shorter time to maturity ------------- B....

VIII. Quant Interview Questions · 14. November 2023

In the intricate world of stochastic calculus, a key question arises: does the derivative dWt/dt exist for Brownian Motion Wt? The answer is intriguing.

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

VIII. Quant Interview Questions · 13. November 2023

Navigating the Quant Interview: Essential Topics and Questions. ✅ ———- Give an estimate for an at-the-money call option on a stock without dividends, with low interest rates and near-term expiration. ———- In the Black-Scholes model, the call option value c is typically: c = S * N(d1) - e^(-rT) * K * N(d2) where: • S is the current stock price, • K is the strike price, • N(.) is the cumulative normal distribution function, • r is the risk-free interest rate, • T is the...

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