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FBE459_3_6_Hedging_Options

# FBE459_3_6_Hedging_Options - FBE 459 Financial Derivatives...

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FBE 459 – Financial Derivatives Prof. Pedro Matos Lecture 3.6.: Hedging Options Portfolio insurance Delta-hedging Greeks Readings: HULL chapter 17

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2 Lecture Outline Portfolio insurance Delta-hedging Greeks
3 Portfolio Insurance Examples: A mutual fund manager owns a portfolio of stocks which he wants to protect against a fall in prices. • A pension fund manager wants to make sure his assets will exceed his liabilities in spite of interest rate and stock price changes.

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4 Portfolio Insurance 1. Static portfolio insurance: > Hold stocks and buy put option on index [ S + p ]. S T K S T K S T K + = LONG STOCK LONG PUT PROTECTIVE PUT
5 Portfolio Insurance 2. Dynamic portfolio insurance: > Dynamically rebalance the portfolio of stocks and T- bonds to replicate a put option on the portfolio. How to replicate S + p ? S + p = S + Ke -rT N(-d2 ) - SN (- d1 ) = S (1 - N(-d1)) + Ke -rT N(-d2 ) = S N ( d1 ) + Ke -rT N ( -d2 ) \$ invested in T-bonds \$ invested in stocks

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6 Portfolio Insurance 2. Dynamic portfolio insurance: > Dynamically rebalance the portfolio of stocks and T- bonds to replicate a put option on the portfolio. • When the market rises, sell T-bonds to purchase stocks • When the market falls, sell stocks to buy T-bonds
7 Portfolio Insurance 2. Dynamic portfolio insurance: > Remember: works only for small changes in S ! > Requires frequent rebalancing, which implies higher transaction costs !

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8 Portfolio Insurance 2. Dynamic portfolio insurance: > When can portfolio insurance go wrong? -> Debate over whether portfolio insurance caused the 1987 crash: read Rubinstein_1987Crash.pdf !
9 Portfolio Insurance: Application Structuring an Equity-Linked Note: > Motivation: retail investors want a share of stock market gains but want their capital protected > An equity-linked note (ELN) is a contract that pays a guaranteed minimum return plus a proportion of the appreciation in an underlying stock or stock index

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10 Portfolio Insurance: Application Structuring an Equity-Linked Note: – Underlying stock or stock index, S – Principal amount, P – Guaranteed return, g – Participation in equity gains if the underlying rises, x – Maturity, T
11 Portfolio Insurance: Application Structuring an Equity-Linked Note: . How to “synthethise” this for your client:

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