The Greek Letters. 14. Chapter Fourteen. This chapter covers the way in which traders working for financial institutions and market makers on the floor of an exchange hedge a portfolio of derivatives.
The software, DerivaGem for Excel, can be used to chart the relationships between any of the Greek letters and variables such as S0, K, r, s, and T.Executive Summary
T = 20 weeks, m = 13%
Take no action:
wait for expiry and “hope for the best”
Buy 100,000 shares today
this amounts to a covered call position
Both strategies leave the bank exposed to significant risk.
Put-call parity shows that the exposure from writing a covered call is the same as the exposure from writing a naked put.
This deceptively simple hedging strategy does not work well in practice:
Purchases and subsequent sales cannot be made at K.
Transactions costs could easily eat the option premium and then some.
e– qT[N (d1) – 1]
D of call
D of put
dP»Qdt + ½GdS2
For a portfolio of derivatives on a stock paying a continuous dividend yield at rate q
A scenario analysis involves testing the effect on the value of a portfolio of different assumptions concerning asset prices and their volatilities
The strategy did not work well on October 19, 1987...
Trading itself is a cause of volatility.
Portfolio insurance schemes such as those just described have the potential to increase volatility.
When the market declines, they cause portfolio managers to either sell stock or to sell index futures contracts. Either action may accentuate the decline.
Selling obviously carries the potential to drive down prices
The sale of index futures contracts is liable to drive down futures prices, this creates selling pressure on stocks via the index arbitrage mechanism.
Whether the portfolio insurance schemes affect volatility depends on how easily the market can absorb the trades that are generated by portfolio insurance.
Widespread use of portfolio insurance could have a destabilizing effect on the market—which would of course increase the necessity of portfolio insurance.