Option Strategist Exercise 3: exploring volatility spreads
In this exercise we will examine the effects of changes in market variables on a variety of volatility spreads. This will also give you practice in setting up positions which involve more than one option.
Underlying: GBP/USD
Price quoted in USD
Contract size: £1,000
European Option
Options on cash
One tick = 1/10,000 of quoted price
Value of one tick = 0.1 USD
USD Year basis = 360 days
GBP Year basis = 365 days
For all of the following positions use 1000 contracts (£1,000,000) per leg of the spread
Buy a call ratio backspread (ratio 2:1) with 1.69 and 1.75 strike 30 day options.
Cable spot rate 1.69
Volatility 20%
US Interest Rates 5%
UK Interest Rates 5%
What view of the market is the trader taking and what position is the seller of this spread taking?
Bullish on direction, long volatility, but the trade is done for a net credit (ATM short strike is worth more than the 2 OTM long strikes). The seller, who is long a call vertical spread is short vol, short delta.
What are the delta and vega exposures in % and £?
Delta = +5%, Vega, +.13%
c) For the following levels of spot write down the delta exposure and the P&L. Explain what you observe.
Spot
Delta exposure%
P&L
1.71
11.6
+1600
1.75
28.5
9300
1.78
42.8
20100
1.60
-5.3
2000
1.63
-4.7
500
1.69
5
0
For the following spot rates and days elapsed, write down the P&L of the backspread. Where is time decay greatest?:
5 days
10 days
15 days
20 days
29 days
1.69
-2300
-4600
-6600
-8000
-1400
1.75
5300
400
-5100
-12300
-39700
1.80
25200
20200
14700
8000
-4300
1.65
-1100
-1500
-1300
-300
5600
1.60
2300
2700
3600
4800
5700
Note that at 30 days when the spot is 1.69, the P&L is +5700, because the rate of decay of the short ATM strike overtakes that of the 2 long OTM strikes. Time decay is greatest when spot is 1.7500.
What happens to the positions P&L as you increase the implied volatility? At what spot rate is the position most sensitive to changes in implied volatility? Why is this the case?
It increases because the position is net long vega. It should be most sensitive at 1.7500, as there is twice the vega exposure at this strike
Set both the initial spot and current spot to 1.75 and buy a put ratio backspread (ratio 2:1) with 1.69 and 1.75 strike 30 day options. What view of the market is the trader taking (and the seller)?
Long volatility, short delta. The seller is short vol long direction and is long a put vertical spread
What are the delta and vega exposures in % and £?
Delta = -3.6%, Vega = .12%
b) For the following levels of spot write down the delta exposure and the P&L. Explain what you observe.
Spot
Delta exposure%
P&L
1.71
-16.7
3800
1.75
-3.6
0
1.78
2.3
-200
1.60
-70.4
51700
1.63
-56.3
32600
1.69
-25.6
8000
For the following spot rates and days elapsed, write down the P&L of the backspread. Where is time decay greatest?:
5 days
10 days
15 days
20 days
29 days
1.69
4100
-400
-5500
-12400
-38600
1.75
-2200
-4200
-6000
-7300
-100
1.80
0
-300
500
2000
7200
1.65
18200
13600
8000
1500
-12600
1.60
48600
45400
42200
39400
37200
Decay is greatest at 1.6900
What happens to the positions P&L as you increase the implied volatility? At what spot rate is the position most sensitive to changes in implied volatility? Why is this the case?
It increases, because the position is long vega. It is most sensitive at 1.6900, because there are 2 ATM options therefore double the vega.
Set both the initial spot and current spot to 1.75 and buy a call ratio vertical spread (ratio 2:1) with 1.69 and 1.75 strike 30 day options. What view of the market is the trader taking?
Bearish on direction and vo.l
What are the delta and vega exposures in % and £?
Delta- -28.5%, vega -.24%
b) For the following levels of spot write down the delta exposure and the P&L. Explain what you observe.
Spot
Delta exposure
P&L
1.71
-11.6
7700
1.75
-28.5
0
1.78
-42.8
-10800
1.60
5.3
7300
1.63
4.7
8800
1.69
-5
9300
c) For the following spot rates and days elapsed, write down the P&L of the vertical spread. Where is time decay greatest?:
5 days
10 days
15 days
20 days
29 days
1.69
11600
13900
15900
17300
10700
1.75
4000
8900
14400
21600
49000
1.80
-15900
-10900
-5400
1300
13600
1.65
10400
10800
10600
9600
3700
1.60
7000
6600
5700
4500
3600
d) What happens to the positions P&L as you increase the implied volatility? At what spot rate is the position most sensitive to changes in implied volatility? Why is this the case?
It decreases because the position is net short vega. It is most sensitive at 1.7500, because it is short 2 ATM options at that spot arte
Set both the initial spot and current spot to 1.69 and buy a put ratio vertical spread (ratio 2:1) with 1.69 and 1.75 strike 30 day options. What view of the market is the trader taking?
Short vol and bullish on direction
What are the delta and vega exposures in % and £?
Delta = 25.6%, Vega = .22%
b) For the following levels of spot write down the delta exposure and the P&L. Explain what you observe.
Spot
Delta exposure
P&L
1.71
16.7
4200
1.75
3.6
8000
1.78
-2.3
8200
1.60
70.4
-43700
1.63
56.3
-24600
1.69
25.6
0
c) For the following spot rates and days elapsed, write down the P&L of the vertical spread. Where is time decay greatest?:
5 days
10 days
15 days
20 days
29 days
1.69
3900
8400
13500
20400
46600
1.75
10200
12200
14000
15300
8100
1.80
8000
8100
7500
6000
800
1.65
-10200
-5600
0
6500
20600
1.60
-40600
-37400
-34200
-31400
-29200
What happens to the positions P&L as you increase the implied volatility? At what spot rate is the position most sensitive to changes in implied volatility? Why is this the case?
The P&L decreases because this position is net short vega. It should be most sensitive at 1.6900, because we are short two ATM puts at that level of spot.
Set the spot rates back to 1.71. Set up a long butterfly spread using 30 day calls with 1.69, 1.71 and 1.73 strikes. What do you notice about the greek exposures and what market conditions would maximise P&L on this position?
The greek exposures almost all cancel out. The most important one from a P&L perspective, Theta, is actually 0. This is because the strikes are too close together.
Set the spot rates back to 1.71. Set up a short butterfly spread using 30 day calls with 1.69, 1.71 and 1.73 strikes. What do you notice about the greek exposures and what market conditions would maximise P&L on this position?
Same as above except this time it is Vega which is the most important greek, and is close to 0.
7. Set the spot rates back to 1.69. Set up a long time spread with 3 month and 6 month options both with 1.69 strikes. What do you notice about the theta and vega exposures? Why is this the case?
Theta and vega are both positive. Short 3 month +T >Long 6 month –T; Short 3 month -V