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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! Simulation

Exchanges: 

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

CBOT: 

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)

CME: 

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)

NYBOT: 

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

NYMEX: 

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

Positions: 

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

Documented Security Information: 

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

Option Valuation: 

Option Valuation Black and Scholes Call Pricing Put-Call Parity Variations

Option Pricing: Calls: 

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

Call Option Pricing Example: 

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

Put Option Pricing: 

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

Black-Scholes Variants: 

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!

Determinants of the Option Premium: 

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  ↑