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2009

Monte Carlo Simulations on Asian Basket Multi Digital Options. Analytical Finance I MMA- 707 Seminar. Group Members Artem Rybakov Moazam Riaz Shoaib Hashmi Simon Porras. Presented to: Jan Röman. 2009. The Task.

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2009

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  1. Monte Carlo Simulations on Asian Basket Multi Digital Options Analytical Finance I MMA- 707 Seminar • Group Members • Artem Rybakov • Moazam Riaz • Shoaib Hashmi • Simon Porras Presented to: Jan Röman 2009

  2. The Task • Build an application in Excel/VBA to solve option prices for an Asian-Basket-Multi-Digital option. That is; an option with maturity in 6 months on a basket of N (say 10) shares.

  3. Concepts & Definitions

  4. Asian Basket Multi Digital Options • Exotic options, composed of many (say 5 , 10) underlying stocks. • Types of Asian Digital Options

  5. Payoffs Illustration of one simulation...

  6. Quantitative Justification: Strong Law of Large Numbers Motivation… • Fundamental Theorem of Arbitrage- free Pricing. • Brownian Motion Assumption for Underlying Stock Price. Price Path Sampling

  7. General Procedure to obtain Expected Payoff of Option Generate a “large” number of Price Paths. Calculate the payoff for each simulation. Estimate the expected value of the option as:

  8. The Strong Law of Large Numbers Proof…

  9. Contd…

  10. Monte Carlo Simulations And Its Applications

  11. Underlying Asset Pricing Formula

  12. Data, Results And Comaprisons

  13. Volatility & Risk Free Interest Rates where… St is a time t stock price St-1 is a time (t-1) stock price N is a number of prices in the interval the volatility is calculated on k is an amount of time frames in 1 year (253 trading days) The risk free interest rate has been chosen in correspondence with coupon interest rate on long-term government bonds. r=7%.

  14. MICEX

  15. Comparisons of Results from Real Data Russian Market Simulated prices C= 0,020026 (volatile market) C= 0,067265 (stable market) Price obtained from real data C= 0,9656 (discounted payoff without uncertainty)

  16. Stockholmbörsen

  17. PriceDynamics Stockholmborsen (Real Market Data)

  18. PriceDynamics (One Simulation Results…) Stockholmborsen

  19. No. of Underlying above Strike (100 Simulations) Stockholmborsen

  20. PriceDynamics (One Simulation Results…) Russian Market

  21. No. of Underlying above Strike (100 Simulations) Russian Market

  22. Questions? 2009

  23. Tack så mycket 2009

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