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Advanced Hedging Strategies Using Black-Scholes and Monte Carlo Simulation Techniques

This paper explores effective hedging strategies through the Black-Scholes model and Monte Carlo simulations. We introduce the fundamental principles of Geometric Brownian Motion (GBM) and demonstrate how it is applied to estimate option prices and manage risk. With a detailed methodology, we generate random trials to analyze stock prices, call prices, and portfolio values. Our findings highlight the dynamics of option pricing in relation to underlying stock prices and emphasize the importance of delta hedging in reducing financial risk.

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Advanced Hedging Strategies Using Black-Scholes and Monte Carlo Simulation Techniques

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Presentation Transcript

  1. Hedging with Black and scholes Analytical Finance I Ellen Bjarnadóttir, Helga Daníelsdóttir and Koorosh Feizi

  2. Introduction • Our assignment • Tools used to solve the problem • Monta Carlo simulation • Geometric Brownian motion (GBM) • Black-Scholes model • Delta hedge

  3. Monte Carlo simulation • Model that gives you possible result using random variables • Calculating probabilty of random outcomes

  4. Black and Scholes • Calculates the option price

  5. Geometric Brownian Motion • Calculates the stock price

  6. Delta Hedge • Changes in option price with respect to underlying stock price • Reduces risk

  7. Methodology • Specify a model • GBM • Black & Scholes • Parameters • S, K, r, σ, T • Generate random trials • Process the output/results • Stock Price - 102 • Call Price – 15,07 • Portfolio Value - 62.831 • Rebalance – 9 times

  8. Stock Price at maturity

  9. Conclusion • Summary • Interpretation of our result • Improvements

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