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 Financial engineering = financial analytics  Lab on Thursday  Easy meter

 Name, Major  Objectives from the class  Things you like about the class  Things that can be improved  Strengths / Attitude towards the Tournament

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Auditing Disaster planning Insurance Risk Mitigation Diversification Business continuity Hedging & Options

is a contract giving the buyer the right, but not the obligation, to buy or sell an underlying asset (for example a stock) at a specific price on or before a specified date  Options are derivatives.

Source: CBOE & OCC web site – Table includes CBOE + C2 combined  CBOE trades options on 3,300 securities. More than 50,000 series listed.  1/4 of US option trading  Hybrid market: 97% total (68% volume) is electronic Year 2013

 You own 100,000 GOOGLE stocks. $1,200 -> $120,000,000.  You are pretty happy.  But you are also worried. What if the price drops to $1,000?  You need some kind of insurance against that.  Somebody is willing to commit to buying your GOOGLE stock at $1,200 (if you want), two years from now.  But she wants $10 per stock. Now.  You decide that it is a good deal. So, you buy 100,000 contracts that give you the choice to sell your stock at the agreed price two years from now.  You have bought 100,000 put options.

 A put option gives to its holder the right to sell the underlying security at a given price on or before a given date.  "Insurance" analogy

 Speculators  Arbitrageurs  Hedgers (us)

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 You are an executive at the Coca Cola Company.  You make $1,000,000 a year.  You are pretty happy.  The Board wants to make sure that you will do your best to keep the price of the CocaCola stock up.  Rather than giving you a well-deserved raise, they offer to you a deal. They promise that in three years they will give you the chance to buy 200,000 stocks at $40.  Right now the stock is valued at $40.  If the company does well, the stock price could go as up as $50.  So you think: “In three years I could just get my $40 and then immediately sell them back to the market for $50....”  You conclude that an extra $2,000,000 in your pocket is a good thing.  You have been given 200,000 call options.

 A call option gives to its holder the right to buy the underlying security at a given price on or by a given date  "security deposit" analogy

IBM Stock Price: $ underlier “spot” (i.e., market) price Call Option can buy 1 IBM $ on 5 Mar 2014 Put Option can sell 1 IBM $ on 18 Apr 2014 strike price expiration: European vs. American option price = premium

IBM Stock Spot Price: $ Call Option can buy 1 IBM $ today Call Option can buy 1 IBM $ today Call Option can buy 1 IBM $ today In the money At the money Out of the money

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 On expiration day, value is certain and dependent on (= strike – spot)  On any other day value is not deterministic, because of uncertainty about the future.

Put Option: Can sell IBM for $200 The current value of a Put Option depends on: 1) the current price of the underlier - 2) the strike price + 3) the underlier volatility + 4) the time to expiration + 5) the risk-free interest rate - IBM’s price is $205 NOWEXPIRATIONPAST Bought a put option on IBM for $1 x = $200 a) IBM’s market price is $190 b) IBM’s market price is $210 Question: what is the value of the option right now?

P = –S[N(–d1)] + Xe -rt [N(–d2)] d1 = {ln(S/X) + (r +  2 /2)t}  t d2 = d1 -  t P = value of a European put option, S = current spot price, X = option “strike” or “exercise” price, t = time to option expiration (in years), r = riskless rate of interest (per annum),  = spot return volatility (per annum), N(z) = probability that a standardized normal variable will be less than z. In Excel, this can be calculated using NORMSDIST(d). Delta for a Call = N(d1) Delta for a Put = N(d1) -1

z

 Example: S = $ 42, X = $40 t = 0.5 r = 0.10 (10% p.a.) s = 0.2 (20% p.a.)  Output: d1 = d2 = N(d1) = N(d2) = C = $4.76 and P=$0.81

 Unlimited borrowing and lending at a constant risk-free interest rate.  The stock price follows a geometric Brownian motion with constant drift and volatility.  There are no transaction costs.  The stock does not pay a dividend.  All securities are perfectly divisible (i.e. it is possible to buy any fraction of a share).  There are no restrictions on short selling.  The model treats only European-style options.

The current value of a call Option depends on: 1) the current price of the underlier + 2) the strike price - 3) the underlier volatility + 4) the time to expiration + 5) the risk-free interest rate + CocaCola’s price is $40 NOWEXPIRATION Call Option: Can buy CocaCola for $40 PAST Bought a call option for $2.00, x=40 a) CocaCola’s price is $45 b) CocaCola’s price is $35 Question: what is the value of the option right now?

C = S[N(d1)] – Xe -rt [N(d2)] d1 = {ln(S/X) + (r +  2 /2)t}  t d2 = d1 -  t C = value of a European call option S = current spot price, X = option “strike” or “exercise” price, t = time to option expiration (in years), r = riskless rate of interest (per annum),  = spot return volatility (per annum), N(z) = probability that a standardized normal variable will be less than d. In Excel, this can be calculated using NORMSDIST(z). Delta for a Call = N(d1) Delta for a Put = N(d1) -1

 Market listed: bid & ask  Buyer & seller: holder & writer  Long & short positions  Blocks of 100 – NOT FOR THE TOURNAMENT  Option class: defined by the underlier and type  Option series: defined by an expiration date & strike example: APPL May Call 290  Expiration: Sat after the 3rd Friday of the month America vs European (TOURNAMENT)  Transaction costs: commissions on trading and exercising.