Page 165 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Derivatives & Risk Management

Notes for options with short maturity, gamma is high and the value of the options changes very fast
with swings in the underlying prices.

Example: Assume the gamma of an option is 0.03 and its delta is 0.4. For a unit change in
the price of the underlying, the delta of the option would change to 0.4 + 0.03 = 0.43. The new
delta of the option at changed underlying price is 0.43; so the rate of change in the premium has
increased.

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 
 

12.1.3 Option Vega

Vega measures the calculated option value's sensitivity to small changes in volatility. In other
words, option Vega indicates how much the option premium would change for a unit change in
annual volatility of the underlying. Vega is positive for a long position (long call and long put)
and negative for a short position (short call and short put). Simply put, for the buyer it is
advantageous if the volatility increases after he has bought the option. On the other hand, for the
seller any increase in volatility is dangerous as the probability of his option getting in the
money increases with any rise in volatility.

Example: Suppose the vega of an option is 0.6 and its premium is 15, when volatility of
the underlying is 35%. As the volatility increases to 36%, the premium of the option would
change upward to 15.6.

/2)
Vega 
2
12.1.4 Rho and Phi

The rho may be defined as the rate of change in the value of option premium to the domestic
interest.
Rho =  option premium/domestic interest rate
Phi is defined as the change in option value (premium) to the change in foreign interest rate.

Phi = option premium /foreign interest rate
TE
Rho  rt 
e

Self Assessment

Fill in the blanks:
1. As the price of the underlying asset rises or falls, options are more or less likely to finish
……………. and their values rise or fall accordingly.
2. As ……….. rises, the extreme outcomes are more likely to increase an option's value.
3. The delta of an option tells you by how much the …………. of the option would increase
or decrease for a unit change in the price of the underlying.

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