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strangecurrency
Topic Author
Posts: 13
Joined: May 12th, 2004, 8:50 am

### Risk Reversals

Hi everybody,I have some questions regarding Risk Reversals.Suppose you have 25 Delta Risk Reversals 1 month EUR-USD -0.09 / 0.19 PMy questions are:1) What do these numbers mean?2) How can I obtain them from the smile? 3) On the Bid Risk Reversals am I available to buy Risk Reversals (that is Buy Call and Sell Put) and on the Offer Risk Reversals am I available to sell Risk Reversals (that is Sell Call and Buy Put)?Thanks for replying.

Anthony
Posts: 237
Joined: September 7th, 2001, 12:04 pm

### Risk Reversals

25D EUR CALL 1 MONTH 11.09 / 11.3825D EUR CALL MID 11.24ATM 1 MONTH 10.94 / 11.1625D EUR PUT 1 MONTH11.14 / 11.4325D RISK REVERSAL BID = 11.14 - 11.24 = -0.10 (dealer buys eur Put sells eur call)25D RISK REVERSAL ASK = 11.43 - 11.24 = 0.19 (dealer sells eur Put buys eur call)i.e. the dealer is giving you a 'choice' market round the mid value of the 25d call and taking the spread relative to the put. The 'P' after the quite means the EUR puts are more expnsive than the EUR calls for that delta. The RR is essentially quoted as a vol spread.Hope this helps.

strangecurrency
Topic Author
Posts: 13
Joined: May 12th, 2004, 8:50 am

### Risk Reversals

Thanks for replying. It helps very much, though I have two more questions:1) you wrote 25D Risk Reversal Bid the dealer buys Eur Put and sells Eur Call. Shouldn't it be the opposite?2) why do the 25D Risk Reversal Bid and Offer are calculated using the Mid Eur Call 25D?Thanks for helping.

Anthony
Posts: 237
Joined: September 7th, 2001, 12:04 pm

### Risk Reversals

1) You might see different conventions on whether you get shown a mid level on the call or a put, but from the example the dealer will buy the Eur put on his/her bid (11.14%) and sell the Eur call at mid 11.24% i.e. the dealer receives 0.10% vol and the customer pays away -0.10% vol. Conversely, the dealer will sell the Eur put on his/her offer (11.43%) and buy the Eur call at mid 11.24% i.e. the dealer receives 0.19% vol. Either way the customer pays on this one!2) The mid value is used (not always on the call) because the dealer is not charging a spread on both legs of the trade, only 1. You'll get one leg of the spread on at mid and then cross the dealers spread on the other.

strangecurrency
Topic Author
Posts: 13
Joined: May 12th, 2004, 8:50 am

### Risk Reversals

Thanks again for replying. I have one last question about this topic:1) How can I calculate the smile curve starting from the Risk Reversals quotes and ATM volatility?Example:RR 25 D 2 Months Eur-Usd: 0.03/0.27 CATM 2 Months Eur-Usd: 10.59/10.80How can I calculate 25 D Eur Call 2 Months (Bid/Ask) and 25 D Eur Put 2 Months (Bid/Ask).

Anthony
Posts: 237
Joined: September 7th, 2001, 12:04 pm

### Risk Reversals

You'll need the butterfly prices to do that. A search on 'Risk Reversal' over the past 6 months will reveal the methodology typically used.

strangecurrency
Topic Author
Posts: 13
Joined: May 12th, 2004, 8:50 am

### Risk Reversals

Thanks Anthony for replying once again.Butterflies can be obtained using this formula:BF 25D (Mid-price) = (25 D Call (Mid-price) + 25 D Put (Mid-price))/2 - ATM (Mid-price)I have also found the formula which allows to calculate the smile curve starting from Risk Reversals, Butterflies and ATM:25 D Call (Mid-price) = (RR 25 D (Mid-price))/2 + BF 25 D (Mid-price) + ATM (mid-price)Now the question is:How can I calculate Bid and Ask of Butterflies?For example, today BF 25 D 3 months Eur-Usd are:Bid 0.11Ask 0.29How do I obtain these numbers?Can you please show me an example?Thanks a lot for helping.

Pat
Posts: 1207
Joined: September 30th, 2001, 2:08 am

### Risk Reversals

Thank you for your response to the risk reversal question. It was helpful.Another market question: what is the convention for bid-ask pricing butterflies? Doe one use mid formulas to get the fly price, and then apply a standard bid ask spread (which seems pretty tight), or does construct them from the a linear combination of call prices, some at the bid side, some at the mid side, and some at the ask side?Thanks

Anthony
Posts: 237
Joined: September 7th, 2001, 12:04 pm

### Risk Reversals

Pat, For a 25 delta butterfly you should use mid levels on the 25 delta calls and puts and then either the bid or ask for twice the notional of the ATM optioni.e. the dealer is earning his/her spread on the ATM option.(mid_25dcall - 2 * BID_ATM + mid_25dput)/2(-mid_25dcall + 2 * ASK_ATM - mid_25dput)/2For the major currencies these should be quoted a few tenths of a vol wide and therefore the above formula might be overidden to tighten the quote or reflect the dealers interest.Hope this helps.

Mircea
Posts: 19
Joined: July 9th, 2004, 6:04 pm

### Risk Reversals

Hi Anthony,From your formula, BF spread = ATM spread, however ICAP quotes for EUR-USD 3M areATM 10.10/10.35RR25D 0.1/0.4BF25D 0.175/0.275Do I miss something?Thanks a lot.

Anthony
Posts: 237
Joined: September 7th, 2001, 12:04 pm

### Risk Reversals

Mircea, As I said you could well see the butterflies quoted tighter than ATM (the risk on the BF is much lower since it is bounded) , you have to be careful with ICAP since they may have sourced the best quotes from various dealers in the market and shown you a bid from one dealer and an offer elsewhere in order to show a quote 1/10 wide. I typically see EUR/USD BF about 2/10 wide.

Mircea
Posts: 19
Joined: July 9th, 2004, 6:04 pm

### Risk Reversals

Anthony. I guess you are right. I was suspecting that. Thanks a lot

averma3
Posts: 2
Joined: November 20th, 2003, 2:53 pm

### Risk Reversals

But still it doesn't explain that butterfly spreads are typically much much lower than Risk reversals and ATM. From Anthony's formula it implies butterfly spreads are same as risk reversal or option spreads....any clues? Arun

InMyWoodenHut
Posts: 32
Joined: November 14th, 2003, 3:34 pm

### Risk Reversals

Take a look at the last few pages of this document hope this helps cheers IMWH

Sawahili
Posts: 17
Joined: November 13th, 2003, 8:37 am

### Risk Reversals

Hi All,Is there an appropriate way to choose the call strike of a risk reversal?Actually, my purpose is simply to play the ATM vol and the skew as purely as possible. The modified risk reversal is constructed in such a way that it has zero gamma. The stock is used in order to get a zero delta.RR = Put(K1) – n * Call(K2)The 3 unknowns are K1, K2 and n.Let’s suppose that K1 is such that Put_Delta(K1) = -25%For a given K2, n is such that the total gamma =0My question is: Is there a criterion to choose K2? K2 could be such that Call_Delta=25%, or 110% of ATM spot, or ….Presently, I am using a symmetry criterion : K1*K2 = Forward^2. But, I have no justification for this.Perhaps there is a mean-variance criterion that could help….Thank you.

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