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Hedging with Black and scholes

Hedging with Black and scholes. Analytical Finance I Ellen Bjarnadóttir, Helga Daníelsdóttir and Koorosh Feizi. Introduction. Our assignment Tools used to solve the problem Monta Carlo simulation Geometric Brownian motion (GBM) Black-Scholes model Delta hedge. Monte Carlo simulation.

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Hedging with Black and scholes

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  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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