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Financial Engineering

Financial Engineering. Zvi Wiener mswiener@mscc.huji.ac.il 02-588-3049. Financial Engineering. Zvi Wiener Head of Finance Department The Hebrew University of Jerusalem 02-588-3049, mswiener@mscc.huji.ac.il. Alon Raviv ??? rmidbary@ovedgubi.com. Textbook.

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Financial Engineering

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  1. Financial Engineering Zvi Wiener mswiener@mscc.huji.ac.il 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

  2. Financial Engineering • Zvi Wiener • Head of Finance Department • The Hebrew University of Jerusalem • 02-588-3049, mswiener@mscc.huji.ac.il Alon Raviv ??? rmidbary@ovedgubi.com FE-Wilmott-Ch1-2

  3. Textbook • Paul Wilmott Introduces Quantitative Finance • John Wiley and Sons, 2001 • See also • http://www.wilmott.com • http://www.paulwilmott.com FE-Wilmott-Ch1-2

  4. Money Market Account FE-Wilmott-Ch1-2

  5. Forward contract (1.9.1) • Asset is traded at $S0 (spot price). • What is the forward price at time T? • We can take a loan, buy the asset for $S0 and wait till T. • Or we can enter a forward contract maturing at T with a forward price F. FE-Wilmott-Ch1-2

  6. Forward contract (1.9.1) • Forward contract: • Today (0) sign a forward contract with forward price F. • At time T pay F, get ST. Time 0 T Money 0 ST-F FE-Wilmott-Ch1-2

  7. Forward contract (1.9.1) • Take a loan for $S0, • buy the stock today, • wait till T, • return the loan 0 T -S0 ST +S0 -S0erT FE-Wilmott-Ch1-2

  8. Forward contract (1.9.1) • The forward price (if no carry) should be • FT = S0 erT • If there are storage costs and convenience yield the formula becomes FE-Wilmott-Ch1-2

  9. Derivatives Following Paul Wilmott, Introduces Quantitative Finance Chapter 2 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

  10. Derivatives and Risk Management • Stocks and bonds are securities – issued to raise capital. • Derivatives are contracts, agreements used for risk transfer. FE-Wilmott-Ch1-2

  11. Financial Derivatives • Futures, Forwards, Swaps • Options • European, American, Asian, Parisian • Call, Put • Cap, Floor • Credit derivatives FE-Wilmott-Ch1-2

  12. Types of Financial Risks • Market Risk • Credit Risk • Liquidity Risk • Operational Risk • Legal Risk FE-Wilmott-Ch1-2

  13. Call Option • The right to buy a particular asset for an agreed amount at a specified time in the future. • Payoff = Max(S-E, 0) • Notional • Strike • Maturity • Underlying • Volatility FE-Wilmott-Ch1-2

  14. Put Option • The right to sell a particular asset for an agreed amount at a specified time in the future. • Payoff = Max(E-S, 0) • Time value • Intrinsic value • At-the-Money • In-the-money • Out-of-the-money FE-Wilmott-Ch1-2

  15. Common terms • Long and Short positions • Margin • Early exercise • Put-Call parity FE-Wilmott-Ch1-2

  16. Value of an Option at Expiration E. Call X Underlying FE-Wilmott-Ch1-2

  17. Call Value before Expiration E. Call X Underlying FE-Wilmott-Ch1-2

  18. E. Call premium X Underlying Call Value before Expiration FE-Wilmott-Ch1-2

  19. Put Value at Expiration E. Put X X Underlying FE-Wilmott-Ch1-2

  20. E. Put X premium X Underlying Put Value before Expiration FE-Wilmott-Ch1-2

  21. Speculation • S=$666 • Call with strike 680 and 4M to maturity is $39 • If you expect the stock price to raise • Buy the stock for 666, sell it for 730 • Have (730-666)/666 = 9.6% profit in 4M • If you buy the option you get • (730-666-39)/39 = 28% on ($39) FE-Wilmott-Ch1-2

  22. Binary (Digital) Call option K S FE-Wilmott-Ch1-2

  23. Binary (Digital) Put option K S FE-Wilmott-Ch1-2

  24. Bull Spread K S FE-Wilmott-Ch1-2

  25. Bear Spread K S FE-Wilmott-Ch1-2

  26. Straddle option K S FE-Wilmott-Ch1-2

  27. Strangle option S FE-Wilmott-Ch1-2

  28. Buttrefly S FE-Wilmott-Ch1-2

  29. Condor S FE-Wilmott-Ch1-2

  30. Warrants • Dilution effect • Endowment warrants • Perpetual warrants Convertible bonds FE-Wilmott-Ch1-2

  31. Collar • Firm B has shares of firm C of value $200M • They do not want to sell the shares, but need money. • Moreover they would like to decrease the exposure to financial risk. • How to get it done? FE-Wilmott-Ch1-2

  32. Collar • 1. Buy a protective Put option (3y to maturity, strike = 90% of spot). • 2. Sell an out-the-money Call option (3y to maturity, strike above spot). • 3. Take a “cheap” loan at 90% of the current value. FE-Wilmott-Ch1-2

  33. Collar payoff payoff K 90 90 100 K stock FE-Wilmott-Ch1-2

  34. Options in Hi Tech • Many firms give options as a part of compensation. • There is a vesting period and then there is a longer time to expiration. • Most employees exercise the options at vesting with same-day-sale (because of tax). • How this can be improved? FE-Wilmott-Ch1-2

  35. Your option Result Sell a call Long term options payoff K 50 k K stock FE-Wilmott-Ch1-2

  36. Example • You have 10,000 vested options for 10 years with strike $5, while the stock is traded at $10. • An immediate exercise will give you $50,000 before tax. • Selling a (covered) call with strike $15 will give you $60,000 now (assuming interest rate 6% and 50% volatility) and additional profit at the end of the period! FE-Wilmott-Ch1-2

  37. Result Your option exercise Example payoff K 60 50 10 15 26 FE-Wilmott-Ch1-2

  38. Home assignment • Read chapters 1-2. • Visit • www.liffe.com • www.nyse.com • www.cboe.com FE-Wilmott-Ch1-2

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