期权应用教程(九)
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Example 4: Bonus question: Stock is at 100 - Does a 100 call have a maximum value? - How can you lock in profit if it trades above this value?
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10
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• Adjust model parameters in response to trades: - When we continuously sell options, raise ATM volatility - When we only repurchase upside calls, increase the slope - If we now buy deep OTM puts lower the put curvature - Etcetera
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Future market: 22,040 – 22,050 Call Bid 1,000 140 Call Ask 1,010 160 STRIKE 21,000 22,000 Put Bid 10 100 Put Ask 20 120
20
40
23,000
970
980
© True Partner Education Ltd 2014
C U H
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1) Finding Risk-Free Arbitrage Opportunities 2) (Statistical ) Volatility Arbitrage: One underlying 3) (Statistical ) Volatility Arbitrage: Multiple underlyings
12
© True Partner Education Ltd 2014
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Vol Arb: implied vs realized
Example: Current S&P 500 •Situation: March implied vol (around at-the-money) is about 32 •Historically (close to close): - 90 day his vol 34 - 360 day his vol 21 • Opinion: you believe 2% per day is too much, markets are calming down, will be moving on average at about vol 24. •Position: Go gamma short (vega short)/ receiving theta •Result on gammashort if true (implied vol staying the same): - Average daily theta ‘in the pocket’: 1-(24/32)^2=44% of theta •Quicker profit possible if implied vols drop (on vega short) to 24: - Expected average theta profit already reflected in lower option price - Profit can be locked in without having to wait until expiration. -“Edge” is gone
C U H
K
20
40
23,000
970
980
© True Partner Education Ltd 2014
4
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
Example 1: Hang Seng December Options - Buy 21,000 call at 1,010 - Sell one future at 22,040 Maximum profit is 21,030 ! (long call, short future = long put)
5
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
Example 2: CCB December Options No dividend, interest rate = 0 %
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CCB: 6.79 – 6.80 Call Bid Call Ask STRIKE Put Bid Put Ask
=> We trade around market volatilities, but do not form an opinion about market volatilities
2
© True Partner Education Ltd 2014
Volatility Arbitrage
When we analyse the market prices and volatilities, we have tools available to form an opinion about these prices and volatilities and thus locate arbitrage opportunities.
0.40
0.30
0.50
0.35
6.50
7.00
0.10
0.30
0.20
0.40
6
© True Partner Education Ltd 2014
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
Example 2: CCB December Options No dividend, interest rate = 0 %
STRIKE 6.50 7.00
Put Bid 0.10 0.30
Put Ask 0.20 0.40
7
© True Partner Education Ltd 2014
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
Example 3: American vs European style (HSBC) Dividend tomorrow of 2.00, before expiration Is there an opportunity when options are European style? Is there an opportunity when options are American style? HSBC: 79.95 – 80.00
Example 3: American vs European style (HSBC) Dividend tomorrow of 2.00, before expiration American style: - buy the call at 9.00 and sell stock at 79.95 - exercise the call and buy stock at 70.00 European style: - sell call at 8.50, buy put at 0.05 and buy stock at 80.00 - profit of 0.45 as future is 78.00
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Call Bid
8.50
Call Ask
9.00
STRIKE
70.00
Put Bid
0.00
Put Ask
0.05
8
© True Partner Education Ltd 2014
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
3
© True Partner Education Ltd 2014
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
Questions to be answered: - What is the opportunity - How do you lock it in - How much money do you make Example 1: Hang Seng December Options Future market: 22,040 – 22,050 Call Bid 1,000 140 Call Ask 1,010 160 STRIKE 21,000 22,000 Put Bid 10 100 Put Ask 20 120
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HSBC: 79.95 – 80.00 Call Bid Call Ask STRIKE Put Bid Put Ask
8.50
9.00
70.00
0.00
0.05
9
© True Partner Education Ltd 2014
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
C U H
K
Sounds complicated but has been discussed before…
11
wk.baidu.com
© True Partner Education Ltd 2014
C U H
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Vol Arb: implied vs realized
Remember lecture 5 ! •Premium Long (a.k.a. Gamma Long) - My gamma revenue is generated by the Realized Volatility - My theta payment is defined by the Implied Volatility I earn money as long as my Realized Volatility exceeds Implied •Premium Short (a.k.a. Gamma Short) - My theta receipt is defined by the Implied Volatility - My losses from gamma are generated by the Realized Volatility I earn money as long as my Realized Volatility is below Implied While mostly the day-to-day movement is taken as a proxy for Realized Volatility, you have seen in the Trading Example that in reality, the results from gamma hedging can significantly differ.
© True Partner Education Ltd 2014
Volatility Arbitrage
(Statistical) Volatility arbitrage: One Underlying
- Implied Volatility vs Realized Volatility - Time Spreads / Forward Volatility (earnings) - Volatility curve
C U H
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Buy Put 7.00 and sell Call 7.00 for a debit of 0.10. Buy the stock at 6.80
Profit 0.10 per share CCB: 6.79 – 6.80 Call Bid Call Ask 0.40 0.30 0.50 0.35
Derivatives Trading: Analysis and Strategies
C U H K
Volatility Arbitrage
1
© True Partner Education Ltd 2014
Volatility Arbitrage
Up until now, we have primarily focused on the Market Maker: • Look at the options on ONE instrument • Fit a logical curve for each of the maturities applying the ‘Wing Model’
C U H
K
10
C U H
K
• Adjust model parameters in response to trades: - When we continuously sell options, raise ATM volatility - When we only repurchase upside calls, increase the slope - If we now buy deep OTM puts lower the put curvature - Etcetera
C U H
K
Future market: 22,040 – 22,050 Call Bid 1,000 140 Call Ask 1,010 160 STRIKE 21,000 22,000 Put Bid 10 100 Put Ask 20 120
20
40
23,000
970
980
© True Partner Education Ltd 2014
C U H
K
1) Finding Risk-Free Arbitrage Opportunities 2) (Statistical ) Volatility Arbitrage: One underlying 3) (Statistical ) Volatility Arbitrage: Multiple underlyings
12
© True Partner Education Ltd 2014
C U H
K
Vol Arb: implied vs realized
Example: Current S&P 500 •Situation: March implied vol (around at-the-money) is about 32 •Historically (close to close): - 90 day his vol 34 - 360 day his vol 21 • Opinion: you believe 2% per day is too much, markets are calming down, will be moving on average at about vol 24. •Position: Go gamma short (vega short)/ receiving theta •Result on gammashort if true (implied vol staying the same): - Average daily theta ‘in the pocket’: 1-(24/32)^2=44% of theta •Quicker profit possible if implied vols drop (on vega short) to 24: - Expected average theta profit already reflected in lower option price - Profit can be locked in without having to wait until expiration. -“Edge” is gone
C U H
K
20
40
23,000
970
980
© True Partner Education Ltd 2014
4
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
Example 1: Hang Seng December Options - Buy 21,000 call at 1,010 - Sell one future at 22,040 Maximum profit is 21,030 ! (long call, short future = long put)
5
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
Example 2: CCB December Options No dividend, interest rate = 0 %
C U H
K
CCB: 6.79 – 6.80 Call Bid Call Ask STRIKE Put Bid Put Ask
=> We trade around market volatilities, but do not form an opinion about market volatilities
2
© True Partner Education Ltd 2014
Volatility Arbitrage
When we analyse the market prices and volatilities, we have tools available to form an opinion about these prices and volatilities and thus locate arbitrage opportunities.
0.40
0.30
0.50
0.35
6.50
7.00
0.10
0.30
0.20
0.40
6
© True Partner Education Ltd 2014
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
Example 2: CCB December Options No dividend, interest rate = 0 %
STRIKE 6.50 7.00
Put Bid 0.10 0.30
Put Ask 0.20 0.40
7
© True Partner Education Ltd 2014
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
Example 3: American vs European style (HSBC) Dividend tomorrow of 2.00, before expiration Is there an opportunity when options are European style? Is there an opportunity when options are American style? HSBC: 79.95 – 80.00
Example 3: American vs European style (HSBC) Dividend tomorrow of 2.00, before expiration American style: - buy the call at 9.00 and sell stock at 79.95 - exercise the call and buy stock at 70.00 European style: - sell call at 8.50, buy put at 0.05 and buy stock at 80.00 - profit of 0.45 as future is 78.00
C U H
K
Call Bid
8.50
Call Ask
9.00
STRIKE
70.00
Put Bid
0.00
Put Ask
0.05
8
© True Partner Education Ltd 2014
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
3
© True Partner Education Ltd 2014
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
Questions to be answered: - What is the opportunity - How do you lock it in - How much money do you make Example 1: Hang Seng December Options Future market: 22,040 – 22,050 Call Bid 1,000 140 Call Ask 1,010 160 STRIKE 21,000 22,000 Put Bid 10 100 Put Ask 20 120
C U H
K
HSBC: 79.95 – 80.00 Call Bid Call Ask STRIKE Put Bid Put Ask
8.50
9.00
70.00
0.00
0.05
9
© True Partner Education Ltd 2014
Volatility Arbitrage
Risk-Free Arbitrage Opportunities
C U H
K
Sounds complicated but has been discussed before…
11
wk.baidu.com
© True Partner Education Ltd 2014
C U H
K
Vol Arb: implied vs realized
Remember lecture 5 ! •Premium Long (a.k.a. Gamma Long) - My gamma revenue is generated by the Realized Volatility - My theta payment is defined by the Implied Volatility I earn money as long as my Realized Volatility exceeds Implied •Premium Short (a.k.a. Gamma Short) - My theta receipt is defined by the Implied Volatility - My losses from gamma are generated by the Realized Volatility I earn money as long as my Realized Volatility is below Implied While mostly the day-to-day movement is taken as a proxy for Realized Volatility, you have seen in the Trading Example that in reality, the results from gamma hedging can significantly differ.
© True Partner Education Ltd 2014
Volatility Arbitrage
(Statistical) Volatility arbitrage: One Underlying
- Implied Volatility vs Realized Volatility - Time Spreads / Forward Volatility (earnings) - Volatility curve
C U H
K
Buy Put 7.00 and sell Call 7.00 for a debit of 0.10. Buy the stock at 6.80
Profit 0.10 per share CCB: 6.79 – 6.80 Call Bid Call Ask 0.40 0.30 0.50 0.35
Derivatives Trading: Analysis and Strategies
C U H K
Volatility Arbitrage
1
© True Partner Education Ltd 2014
Volatility Arbitrage
Up until now, we have primarily focused on the Market Maker: • Look at the options on ONE instrument • Fit a logical curve for each of the maturities applying the ‘Wing Model’