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user25844
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and thank you for answering me !

While I was recently testing a delta-hedging on a few products, I got a P&L result of 20% for some of them.

First, I thought that the implementation was incorrect. But I couldn't find an outright error.

After a deeper look in my (back)test-data, I found that delta-hedging might not be enough even for simple products like 'vanilla calls'.

Here's an example (with payoff = (S(T) - K )+): (T = 20 days, K =50.5, (hypothesis : Black-Scholes model))

S:

day 0 = 50 ;

day 1 = 50.5 ;

day 2 = 50.3 ;

... ;

day 15 = 52.7 ;

day 16 = 49.3 ;

day 17 = 37.5 ;

day 18 = 36.4 ;

day 19 = 36.8;

day 20 = 37.7.

I rebalance every day and because of the huge price fall on day 17, and because my delta was close to 1, I lost a lot of money (call price is almost 0, while my porfolio is about -15), causing a big P&L.

So, my questions are :

1/ Is it correct that : "delta-hedging is ok for continuous data (and continuous heding). Price-jumps are not hedged with delta-hedging"..?

2/ Assuming that we can't hedge more than once a day, and having recurrent (there are a few) prices falls in my data, what do you suggest for a hedging ?

Thanks a lot, Guillaume

and thank you for answering me !

While I was recently testing a delta-hedging on a few products, I got a P&L result of 20% for some of them.

First, I thought that the implementation was incorrect. But I couldn't find an outright error.

After a deeper look in my (back)test-data, I found that delta-hedging might not be enough even for simple products like 'vanilla calls'.

Here's an example (with payoff = (S(T) - K )+): (T = 20 days, K =50.5, (hypothesis : Black-Scholes model))

S:

day 0 = 50 ;

day 1 = 50.5 ;

day 2 = 50.3 ;

... ;

day 15 = 52.7 ;

day 16 = 49.3 ;

day 17 = 37.5 ;

day 18 = 36.4 ;

day 19 = 36.8;

day 20 = 37.7.

I rebalance every day and because of the huge price fall on day 17, and because my delta was close to 1, I lost a lot of money (call price is almost 0, while my porfolio is about -15), causing a big P&L.

So, my questions are :

1/ Is it correct that : "delta-hedging is ok for continuous data (and continuous heding). Price-jumps are not hedged with delta-hedging"..?

2/ Assuming that we can't hedge more than once a day, and having recurrent (there are a few) prices falls in my data, what do you suggest for a hedging ?

Thanks a lot, Guillaume

While I was recently testing a delta-hedging on a few products, I got a P&L result of 20% for some of them.

First, I thought that the implementation was incorrect. But I couldn't find an outright error.

After a deeper look in my (back)test-data, I found that delta-hedging might not be enough even for simple products like 'vanilla calls'.

Here's an example (with payoff = (S(T) - K )+): (T = 20 days, K =50.5, (hypothesis : Black-Scholes model))

S:

day 0 = 50 ;

day 1 = 50.5 ;

day 2 = 50.3 ;

... ;

day 15 = 52.7 ;

day 16 = 49.3 ;

day 17 = 37.5 ;

day 18 = 36.4 ;

day 19 = 36.8;

day 20 = 37.7.

I rebalance every day and because of the huge price fall on day 17, and because my delta was close to 1, I lost a lot of money (call price is almost 0, while my porfolio is about -15), causing a big P&L.

So, my questions are :

1/ Is it correct that : "delta-hedging is ok for continuous data (and continuous heding). Price-jumps are not hedged with delta-hedging"..?

2/ Assuming that we can't hedge more than once a day, and having recurrent (there are a few) prices falls in my data, what do you suggest for a hedging ?

Thanks a lot,

Tweeted twitter.com/StackQuant/status/846472670690594816
Source Link
user25844
user25844
  • 375
  • 2
  • 15

delta-hedging is failing

and thank you for answering me !

While I was recently testing a delta-hedging on a few products, I got a P&L result of 20% for some of them.

First, I thought that the implementation was incorrect. But I couldn't find an outright error.

After a deeper look in my (back)test-data, I found that delta-hedging might not be enough even for simple products like 'vanilla calls'.

Here's an example (with payoff = (S(T) - K )+): (T = 20 days, K =50.5, (hypothesis : Black-Scholes model))

S:

day 0 = 50 ;

day 1 = 50.5 ;

day 2 = 50.3 ;

... ;

day 15 = 52.7 ;

day 16 = 49.3 ;

day 17 = 37.5 ;

day 18 = 36.4 ;

day 19 = 36.8;

day 20 = 37.7.

I rebalance every day and because of the huge price fall on day 17, and because my delta was close to 1, I lost a lot of money (call price is almost 0, while my porfolio is about -15), causing a big P&L.

So, my questions are :

1/ Is it correct that : "delta-hedging is ok for continuous data (and continuous heding). Price-jumps are not hedged with delta-hedging"..?

2/ Assuming that we can't hedge more than once a day, and having recurrent (there are a few) prices falls in my data, what do you suggest for a hedging ?

Thanks a lot, Guillaume