sims by wangnuanzg

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									Options, Dynamic Strategies
      and Simulations


      FIN285a: Lecture 5.4-5.5
              Fall 2010
  Jorion 6.1-6.2 (6.3 skim),6.4, 6.5
    Monte-carlo Simulations
          Examples
 Harder problems
 Simulations necessary
               Applications
 Simple  option portfolio
 Exotic options (Asian)
     Asian options
     Barrier options
 Pairs   trading
                Code
 putdow.m
 asianopt.m
 barrier.m
 pairstrat.m
      Simple Option Example
 100 shares of Dow
 Current price = 1
 Cover 75 shares with put options
     European
     Expiration in 1 day
 Strike   price = 1 (at the money)
        Two Big Assumptions
 Option   value today
     Assume Black/Scholes formula
 Value   option tomorrow as
     Price increase : Zero
     Price decrease: 1-P(tomorrow)
     Note: this is sensible because of expiration
           Matlab Example
 putdow.m
 Note:
     Very nonnormal distribution
     Importance of VaR when options are
      present
               Applications
 Simple  option portfolio
 Exotic options (Asian)
     Asian options
     Barrier options
 Pairs   trading
 Exotic Option (Asian Option)
 Standard       call option
     Payoff = max(price-strike,0)
 Standard       put option
     Payoff = max(strike-price,0)
 Asian   call
     Payoff = max( mean(price)-strike,0)
 Asian   put
     Payoff = max( strike - mean(price),0)
              Example (matlab)
 Asianopt.m
 European option expiring in 20 days
 Option valuation
       Risk neutral pricing (pp 153-154)
       Monte-carlo
       Use this to get today’s value
       Future value = max(strike-mean(price))
 VaR : usual calculations
 Compare : plain and Asian option
             Risk Neutral Note
   Pt 1  Pt
r                       Pt 1 / Pt  1
       Pt
R  log(Pt 1 )  log(Pt )  log(Pt 1 / Pt )
R ~ N( ,  2 )
                2 /2
E(e )  e
    R


E(r)  E(e R )  1
              2 /2
E(r)  e                1
                        2                 2
E(r)  1                  1  
               2           2
Desired (Risk neutral) mean E(r)  rf (risk free)
           2
  rf 
             2
         Why Asian Option?
 Firm with continuous cash flows over
  the period
 Multinational:
     Ford get BP inflows over month
     Want to cushion average exchange rate,
      not end of period exchange rate
                 Barrier Option
 Option depends on price path again
 Expires or comes to life depending on max or
  min of recent path
 Down and out
       Option expires when price hits lower barrier from
        above
 Down and in
 Up and out
 Up and in
           Barrier Option
 Down  and out put option
 barrier.m
 Similar to Asian example
         Why Use Barrier?
 Exporter  to Japan
 Hedge $/Yen fx rate risk with a put
  option
 If $/Yen rate drops below a certain level,
  then firm closes out export operation -
  don’t need option
 Use a down and out put for this
               Applications
 Simple  option portfolio
 Exotic options (Asian)
     Asian options
     Barrier options
 Pairs   trading
                  Pairs Trading
 Market neutral strategy
 Implementation
       Two stocks that ought to move together
       Short high priced one
       Long low priced one
       Wait
       When (and if) they converge clear out position and
        take profits
               Example
 Simulated   price series
 Two stocks with common factor
 Prices driven by common factor
  (industry) and own factors
 Own factors eventually go away, and
  prices should never get too far apart
 pairsgen.m, pairsplot.m
     Implementing the Strategy
   p1 and p2 = prices
       p1 starts at 100, p2 at 100+spread
 Initially long $100 of p1, and sell $100 of p2
  short
 (Ignore margins, dividends, and transaction
  costs)
 Unwind when p2<p1+stopspread
 Otherwise clear position after maximum days
        VaR versus Liquidity VaR
 Simple discounted end of period value is VaR
 What if there are intermediate cash flows?
       Margin calls on shorts
 For simplicity: model like a futures
 Mark to market each day
       (See picture: next slide)
   Futures would require you to have available
    this much cash
        Marking to Market

price
                    110
                          2
         105

100

               95
                          1
                     90

                              time
                 Example
 pairstrat.m
 Note:
     Great strategy in terms of VaR
     However, may require large amounts of
      cash before it becomes profitable
 VaR  is not the whole story here
 Try changing parameters

								
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