ARTICLES AVEC LE TAG : "III A. Options and Hedging"

VIII. Quant Interview Questions · 14. novembre 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. novembre 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. novembre 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.
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. novembre 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...
Explore the dynamic between intuition & quantitative models in trading. While mathematical strategies are useful, the human brain excels in analyzing volatile stocks, discerning lasting trends from transient ones. Success lies in balancing pattern recognition, historical data, and instinct.
In simple terms, think of hedging like insurance. A bank sold a specific type of "insurance" (Down-and-Out European Call) that pays out only if the stock price doesn't dip below a certain level (the barrier). To safeguard itself, the bank uses a mix of buying and selling other financial "insurances" (call and put options). The magic formula ensures that if the stock dips below the barrier, the bank won't lose money. It's a balancing act, where buying one thing counteracts the selling of another
Bank sells a Knock-Out (KO) call option on Stock XYZ to a bullish trader. If stock hits \$110, the option ends. To hedge risks like vega and vanna from the KO option, the bank uses a Risk Reversal (RR). They buy call options and sell put options on Stock XYZ. This manages volatility changes and price shifts, ensuring stable positions. If the stock reaches \$110, the KO ends with no payout due. The RR helps the bank control risk. #HedgingStrategies #RiskReversal #OptionsTrading #BarrierOptions

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