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Simulation & Black-Scholes Pricing

Simulation & Black-Scholes Pricing. Simulation. Brokerage Account and Live Data from Exchanges Activate Some Strategies Document Intent, Execute and Resolve Make Some Money, Have Some Fun!. Exchanges. Chicago Board of Trade www.cbot.com Chicago Merchantile Exchange www.cme.com

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Simulation & Black-Scholes Pricing

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  1. Simulation & Black-Scholes Pricing

  2. Simulation • Brokerage Account and Live Data from Exchanges • Activate Some Strategies • Document Intent, Execute and Resolve • Make Some Money, Have Some Fun!

  3. Exchanges • Chicago Board of Trade • www.cbot.com • Chicago Merchantile Exchange • www.cme.com • New York Board of Trade • www.nybot.com • New York Merchantile Exchange • www.nymex.com

  4. CBOT • Agricultural • Corn (C), Soybeans (S), Soybean Oil (BO), Soybean Meal (BM), Wheat (W), Oats (O) • Interest Rates • 30 day Fed Funds (FF), 2y (TU), 5y (FV), 10y Notes (TY), 30y Bond (US) • Indexes • Dow Jones 30 (DJ)

  5. CME • Meats • Live Cattle (LC), Feeder Cattle (FC), Lean Hogs (LH), Pork Bellies (PB) • Lumber (LB) • Indexes • Equity: S&P 500 (SP), NASDAQ 100 (ND), Nikkei 225 (NK) • Commodity: Goldman Sachs Commodity Index (GI) • Foreign Exchange • British Pound (BP), Canadian $ (CD), Japanese Yen (JY), Euro (EC) • Interest Rates • Euro$ (ED), T-Bill (TB)

  6. NYBOT • Food & Fiber • Cocoa (CC), Coffee (KC), Sugar-World (SB), FCOJ (OJ) • Cotton (CT) • Indexes (NYFE) • US$-Index (TX)

  7. NYMEX • Energy • Light, Sweet Crude Oil (CL), Heating Oil (HO), Unleaded Gasoline (HU), Natural Gas (NG) • Metals • Gold (GC), Silver (SI), Copper (HG)

  8. Positions • $500,000 portfolio • No more than $150,000 in any one position • At least 3 option and 3 futures trades • 3 options as we discuss options • 3 futures as we discuss futures • Each position must have: • Documented opinion • Documented Security information • Initial Trade Price • Daily Closing Prices • Final Closing Price

  9. Documented Security Information • Contract/Position Size • Contract/Position Value • Last Trading Day of Contract • Contract/Position Initial Margin Deposit

  10. Option Valuation • Black and Scholes • Call Pricing • Put-Call Parity • Variations

  11. Option Pricing: Calls • Black-Scholes Model: C = Call S = Stock Price N = Cumulative Normal Distrib. Operator X = Exercise Price e = 2.71..... r = risk-free rate T = time to expiry = Volatility

  12. Call Option Pricing Example • IBM is trading for $75. Historically, the volatility is 20% (s). A call is available with an exercise of $70, an expiry of 6 months, and the risk free rate is 4%. ln(75/70) + (.04 + (.2)2/2)(6/12) d1 = -------------------------------------------- = .70, N(d1) = .7580 .2 * (6/12)1/2 d2 = .70 - [ .2 * (6/12)1/2 ] = .56, N(d2) = .7123 C = $75 (.7580) - 70 e -.04(6/12) (.7123) = $7.98 Intrinsic Value = $5, Time Value = $2.98

  13. - = - - - rT P Xe N ( d ) SN ( d ) 2 1 Put Option Pricing • Put priced through Put-Call Parity: Put Price = Call Price + X e-rT - S (or : ) From Last Example of IBM Call: Put = $7.98 + 70 e -.04(6/12) - 75 = $1.59 Intrinsic Value = $0, Time Value = $1.59

  14. Black-Scholes Variants • Options on Stocks with Dividends • Futures Options (Option that delivers a maturing futures) • Black’s Call Model (Black (1976)) • Put/Call Parity • Options on Foreign Currency • In text (Pg. 375-376, but not req’d) • Delivers spot exchange, not forward!

  15. Determinants of the Option Premium • Stock price; Call ↑ as S ↑; Put ↑ as S ↓ • Striking price • Call ↑ as X ↓; Put ↑ as X ↑ • Volatility, Time until expiration, Risk-free interest rate • Call/Put ↑ as , , and  ↑

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