Question

The table below gives the price of a six-month put option today, as well as the different Greek letters associated with this price. Given this information, derive your best estimate of the price of the put option five days from now, if during this time the index level decreases from 250 to 244, and the volatility increases from 10% to 15%.

Underlying Type: Index

Index Level: 250

Volatility(% per year): 10%

Risk-Free Rate(% per year): 2%

Dividend Yield(% per year): 1%

Option Type: Black-Scholes - European

Life(Years): 0.5

Strike Price: 250

Results:

Price: 6.3953881

Delta (per $): -0.4554818

Gamma (per $): 0.0223291

Vega (per %): -0.0156472

Rho (per %): -0.6013292

Answer 1

We use Delta, Vega, and Thera to arrive at the put option price

Delta = -0.4554818

Vega = 0.6977835

Theta = -0.0156472

Delta signifies how much the price of an option would change when the spot price of the asset increases by $1

Vega signifies the amount of option's price changes to 1% change in volatility of the underlying asset

Theta is the change in the value of the option due to the passage of time ie. it is the amount by which an option price decreases per day.

For delta, price has decreased by $6

For vega, volatility has increased by 5%

For theta, days to maturity have decreased by 5 days

Taking cumulative effect of the 3 option greeks,

Change in put option price = (5*0.6977835)+(5*(-0.0156472)) + ((-6)*(-0.4554818))

Change in put option price =6.1435723

Hence, the put option value increases by $6.1435723 approximately

New price of the put option = 6.3953881 + 6.1435723

New price of the put option = $12.5389604