Option Strategist Exercise 1: exploring premiums, time value and volatility
In this exercise we will examine the effects of changes in market variables on the premium of a plain vanilla call written on a FTSE 100 stock. We will use the following option contract:
Underlying: Shell (Transport)
Price quoted in GBP
Contract size: 1,000 shares
European Option
Options on cash
One tick = 1/100 of quoted price
Value of one tick = 10GBP
Dividend Year basis = 365 days
Funding Year basis = 365 days
• Using the Options Strategist buy one at-the-money call with 30 days to expiry.
Price of underlying today £8.40
Price of underlying at purchase £8.40
Implied volatility 15%
Initial implied volatility 15%
Shell dividend yield 6%
GBP rate (Libor) 6%
• What is the premium paid
• In pence?
ii) As a percentage of strike?
• What would the premium be if you bought the call at a strike of:
• £8.50
• £8.30
What is the relationship between the strike price and the premium payable?
• What is the value of the £8.40 call at expiry if the underlying is trading at:
• £8.30
• £8.40
iii) £8.50
What does the value of the call at expiry represent?
• What is the profit or loss on the position at expiry for the following prices of the underlying:
• £8.35
• £8.40
• £8.45
• £8.50
• For a call struck at £8.40 with 30 days to maturity, what are the intrinsic and time values at inception, for the following prices of the underlying:
Price £
Time Value
Intrinsic Value
8.40
8.55
8.50
8.45
8.40
8.35
8.30
8.25
Where is time value at its greatest?
• What is the fair value and P&L of the 8.40 call (other things being equal) after the following days have elapsed:
Days Elapsed
Fair Value
P&L
5
10
15
20
25
29
2) Plot the fair value against days elapsed on the following graph:
Option Value
Days Elapsed
• What is the relationship between time to expiry and the value of the call option? Is it linear?
b) Why does a long-dated option have greater time value than a short-dated one?
• What is the fair value and P&L of the £8.40 call for the following levels of volatility:
Volatility
Fair Value
P&L
1%
5%
10%
15%
20%
25%
3)
• Now set up a short position with the 8.40 strike call (just put a – sign in front of the existing position) and repeat the above for P&L only:
Volatility
P&L
1%
5%
10%
15%
20%
25%
• What is the P&L of the short 8.40 call position after the following days have elapsed:
Days Elapsed
P&L
5
10
15
20
25
29
• Now delete the call position and set up a put position on Shell with an £8.40 strike:
i) What is the value of the £8.40 put at expiry if the underlying is trading at:
£8.30
£8.40
£8.50
What is the profit or loss on the position at expiry for the following prices of the underlying:
£8.35
£8.40
£8.45
£8.50
ii) What is the fair value and P&L of the £8.40 put for the following levels of volatility:
Volatility
Fair Value
P&L
1%
5%
10%
15%
20%
25%
iii) What would the premium be if you bought the put at a strike of:
• £8.50
• £8.30
What is the relationship between the strike price and the premium payable?
5) Given the effect of volatility on the fair value of the put and call, would you say it was correct to treat them as equal assets?