Week 11 Finance
Week 11 Finance FIN 500
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This 3 page Class Notes was uploaded by D S on Monday November 30, 2015. The Class Notes belongs to FIN 500 at University of Illinois at Urbana-Champaign taught by Adam Clark-Joseph in Summer 2015. Since its upload, it has received 32 views. For similar materials see Introduction to Finance in Finance at University of Illinois at Urbana-Champaign.
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Date Created: 11/30/15
Introduction to Finance Week 11 Professor ClarkJoseph University of Illinois Urbana Champaign November 30 2015 1 Option Greeks allows us to look at th sensitivity of options pices to changes in relevant parameters variable meta arrow price looking at the scale pictures for calls changes in call or puts option values things are converging to the payofl 7 claim can be made that almost scaled volatility based upon the time decreasing increasing volatility at time today7 amount of lots of time VET volatility 2 Greeks motivation dynamics rebalancer Name Symbol Equation Summary Delta A A share price 82V movements Gamma F F 882 changes in the V6 hDelta ga 1 1 80 c anges in r volatility Rho p p 2 changes in risk free rate Theta 6 changes in time Elasticity e 5 g gtIlt change in option price per unit of change in stock price price of option underlying When in the money binomial tree 6 CLT BSM doesn t really work at the tails out of the money yet that is the area that money markers enjoy this is due to the fact that people nd it dif cult or make it such that you can overprice people and make a pro t why isn t there a Greek for changes in the Strike Price this parameter tends not to change SO and K change predictability taking 8K not as useful but a good exercise rf slightly more interesting since it has raised quite a bit in the past couple months 21 Delta A changes in price of an instrument portfolio resulting from a one unit change in the price of the underlying instrument or rate A number of shares of stock will come from replicating portfolio in path dependent option nding partials is more dif cult had a discussion that for Delta hedging to work need the ability to rebabalance continuously which is impractical NOTE hit Taylor s theorem hard for this 1 partial ff of the actually F Analytical formula for Delta in BSM basically just looks like an S on the curve in relation to the upward exponential trending options price Aczg gzNd1Apg Nd1 1 hedge ratio 7 Why use theoretical pricing model implicit leverage mutual funds loop holes for leveraging up how much exposure can you get buying hedging the options Why are there not any rules against option for 401K Taylor bounded idea that factorial grows faster in most cases 2quot 1 so bounded by n 14 15 toy example that shoes that Delta is a great local measure xed convexity for delta take a look at the out of the money convexity curve short side straddle position undertnad the importance of changing delta i from neg to positive delta is good for small movements 22 Gamma F throw in curvative ie the 2nd order taylor approx econ intuition formality if you want to approx risk variability gamma lt 0 changes in instrument portfolio value will be more adverse than indicated by delta gamma gt change in instrument value will be more favorable than indicated by delta note its te same for both puts and calls F 82V ed2 W maqs kaxCZTIE now have them in a taylor expansion and call it a day the gamma of a stock is zero since delta would be 1 make sure you know how to do the sample interview question even though its easy look at slide 1124 in cse you forget Delta and Gamma summarize market risk in the position look at the pictures Why would you not delta and gamma hedge 23 Vega V change in value resulting from one unit change in volatility this was what the hw assignment was referring to intuitively some relation to Gamma7 its easy but boring algebra able to get exactly why is there so much symmetry among put and call Random Paradox Stieglitz Transform look this up time changes shrinking volatility 24 Theta 9 8V 9 w time derivative Why include F with respect to price but not include 2nd order for other terms Brownian motion sqrtt 1 is order gt 1 order don t really pursue the discrepancy 25 Rho 0 only really used for euro dollars others not that interesting 26 Elasticity 5 useful for returns analysis Delta Hedging look at RS notes on this given that it is important and yet we ve been able to do it already