© Stefano Grazioli - Ask for permission for using/quoting: Stefano Grazioli

 Financial Engineering = Financial analytics  Extended office hours 2-6pm (no 3:15-3:45 today)  Lab Easy meter

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

© Stefano Grazioli - Ask for permission for using/quoting: An introduction (spans two lectures)

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 (e.g., a stock) at a specific price on or before a specified date  Options are derivatives.

 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 Source: CBOE & OCC web site – Table includes CBOE + C2 combined Year 2013

 You own 1,000,000 Apple stocks. $110 -> $110,000,000.  You are pretty happy.  But you are also worried. What if the price drops to $80?  You need some kind of insurance against that.  Somebody is willing to commit to buying your Apple stock at $110 (if you want), two years from now.  But she wants $1 per stock. Now.  You decide that it is a good deal. So, you buy 1,000,000 contracts that give you the choice to sell your stock at the agreed price two years from now.  You have bought 1,000,000 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.  Think insurance

 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 = European)  Transaction costs: commissions on trading and exercising.

 Speculators  Arbitrageurs  Hedgers (us)

© Stefano Grazioli - Ask for permission for using/quoting: What Is New In Technology?

 You are an executive at Netflix.  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 Netflix 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 400,000 stocks at $100 each.  Right now the stock is valued at $100.  If the company does well, the stock price could go as up as $120.  So you think: “In three years I could just get my $100 and then immediately sell them back to the market for $ ”  You conclude that an extra $8,000,000 in your pocket is a good thing.  You have been given 400,000 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  Think "security deposit"

IBM Stock Price: $ underlier “spot” (i.e., market) price Call Option can buy 1 IBM $ on 15 March 2017 Put Option can sell 1 IBM $ on 15 March 2017 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

© Stefano Grazioli - Ask for permission for using/quoting: An introduction

 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 AAPL for $100 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 - APPL price is $105 NOWEXPIRATIONPAST Bought a put option on Apple for $1 x = $100 a) AAPL market price is $120 b) AAPL market price is $80 Question: what is the value of the option right now?

Equilibrium price for a Put = –S[N(–d1)] + Xe -rt [N(–d2)] d1 = {ln(S/X) + (r +  2 /2)t}  t d2 = d1 -  t 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).

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 a 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 + FB price is $100 NOWEXPIRATION Call Option: Can buy FB for $110 PAST Bought a call option on FB for $2.00, x=110 a) FB price is $100 b) FB price is $120 Question: what is the value of the option right now?

Equilibrium Price of a Call = S[N(d1)] – Xe -rt [N(d2)] d1 = {ln(S/X) + (r +  2 /2)t}  t d2 = d1 -  t 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