Simulation & Black-Scholes Pricing

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

Exchanges  Chicago Board of Trade   Chicago Merchantile Exchange   New York Board of Trade   New York Merchantile Exchange 

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

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

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  Contract/Position Size  Contract/Position Value  Last Trading Day of Contract  Contract/Position Initial Margin Deposit

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

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

Call Option Pricing Example  IBM is trading for $75. Historically, the volatility is 20% (  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) d 1 = =.70, N(d 1 ) = * (6/12) 1/2 d 2 =.70 - [.2 * (6/12) 1/2 ] =.56, N(d 2 ) =.7123 C = $75 (.7580) - 70 e -.04(6/12) (.7123) = $7.98 Intrinsic Value = $5, Time Value = $2.98

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

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 , but not req’d)  Delivers spot exchange, not forward!

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  ↑