Variable Annuity, Hedging of Risk

[JMO]

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=100105

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=99668

[wtt]

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=100105

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=99668
JMO, are you also interested in this area? Could you give us your thoughts?

[JMO]

On the subject of delta hedging, it has occurred to me that just when you need it most, it's going to become more expensive. But that's just off the top of my head. I'm not working with annuities these days.

[Eimon Gnome]

The curious side is when the hedge loses.

Presumably, you are out there shorting the market. You want something that pays off dollars if the stock market tanks. Part of the need is from the guarantees in the contract, but a larger part of it is the future M&E streams (a lot of which is used to repay the commission already paid to the agent at closing)
So, as the market soars, your hedges are losing boatloads of money. As it goes higher and higher, your trades are huge cash drains. The offsets - no value to the guarantees and bigger future cash payments on the M&E fees -are purely paper gains. A lowr reserve and a bigger value to future receivables. But funding that hedge loss can get crazy expensive if the market keeps going up.It can mean a whole lot of borrowing.

To me, that is the big risk in a dynamic hedging strat. The liquidity needs can get pretty amazing.

[wtt]

The curious side is when the hedge loses.

Presumably, you are out there shorting the market. You want something that pays off dollars if the stock market tanks. Part of the need is from the guarantees in the contract, but a larger part of it is the future M&E streams (a lot of which is used to repay the commission already paid to the agent at closing)
So, as the market soars, your hedges are losing boatloads of money. As it goes higher and higher, your trades are huge cash drains. The offsets - no value to the guarantees and bigger future cash payments on the M&E fees -are purely paper gains. A lowr reserve and a bigger value to future receivables. But funding that hedge loss can get crazy expensive if the market keeps going up.It can mean a whole lot of borrowing.

To me, that is the big risk in a dynamic hedging strat. The liquidity needs can get pretty amazing.
I start getting difficult to understand this discussion. I feel a good project in the area may be helpful for deeper discussion.

However, I have a simpler question. After the hedging department drew conclusion like this, usually how should you guys convey this analysis to investment division arm of your company?

[Run2standstill]

Just throw in my 2 cents and without going into too much details, the common ways to hedge VA products include

1: Put option

type: at the money put or more often slightly out of money put

Pros: easy to understand
easy to implement and maintain
current low implied volatility enviroment making European type options relatively cheap. Good time to buy options.

Cons: no long term put on the market or extremely expensive

2: delta hedging

Pros: cheaper to implement
works well if things stay relatively stable and consistent

Cons: delta does change frequently, and pure delta hedging ignores the Gamma effect which could be large when market moves big and quick.

Modification: delta-gamma hedging, or delta-gamma+one more Greek (Theta or Vega) hedging

3: dynamic hedging

Pros: adjust static hedging periodly to more accurately hedge the underlying risks

cons: costly, and often need dedicated experts/resources

4: Index future

Pros: often works better and cheaper than buying puts

Cons: still having basis risks that the underlying asset portfolio does not move the way and/or the magnitude that the market changes. (how good is your portfolio's Beta calculation?)

5: Internal product design

For example, selling GMDB together with GMAB

6: New kids on the block

a: total return swap

b: Credit default swap (CDS) - a benign credit enviroment has making the CDS premium very attractive. It could be good portfolio return enhancement.

[MathGeek92]

yes.

It's like buying insurance on your liability

[WWSituation]

When a company writes a guarantee, they are essentially issuing a long-dated put option. The policyholder buys the right to withdraw their account value regardless of how the market does - that is the definition of an option.

It stands to reason that options (long-dated puts) would be the primary hedging vehicles for these programs to the extent that liquidity allows. S&P option market is pretty liquid these days to at least 10 years.

[WWSituation]

So the company has to buy put(often short term ones) to hedge that long-dated put option, right?

If so, how can the company make money from this kind of transaction espeically there are hedging cost, put option buying cost and other expenses?

The company may increase its VA sales by offering that kind of option to policyholder?

The "short term" puts are 10 years out (I wouldn't be surprised if companies like Hartford had many that were even 15 and longer).

The company charges a fee for the rider. Now we would be naive to think that companies charge the correct rate for these - especially since they are usually locked into the price for at least 3-6 months. After M&E and investment management fees, though, it turns out to be a really good deal if the company has the scale to bury the excess hedging costs.

Hartford just posted a huge increase in VA sales and Lincoln is breaking records every quarter with their VA sales - so I'd say that these are really helping them. The increased sales are really fools gold - since they do nothing but raise questions about the quality of the pricing and risk management. Hedging will never get their due credit since the cynic in peoples minds will always be waiting for the "blow up".

[Run2standstill]

10 yr put is almost as far as one can find in the market. Anything beyond that is customer tailored. Since 20yr or 30 yr puts are generally either not available or too expensive, one has to rebalance the put strategy at some point. Locking oneself for long term (10-15yr) option has its own issue as well. For example, S&P was at around 1,200 at the beginning of 2005, and one bought a 15% out of money put. In other words, the put would pay if the index falls below 1200*(1-15%) = 1,020. Now 2 years later, the S&P stood around 1,430. The option one bought last year actually represents a 29% Out-of-Moneyness, which means if the market tanks tomorrow in a scale like in the 1987 crash, the company would have to take the hit naked. So a better strategy is to build a layered put strategy and "dynamically" monitor the short term puts as the underlying liability changes.

[Run2standstill]

"Is that so-called dynamic hedging strategy? Do you have to calculate Greeks over this matter?

It is not a dynamic hedging by a straight defination though it involves rebalancing. I do calculate Greeks quarterly and watch closely how Vega changes in that unlike Delta and Gamma, Vega of hedging portfolio and the underlying could move in the same diretion - reason for that - "Volatility Smile".

[Run2standstill]

Somehow I had the impression that Hartford life has been calculate Greeks weekly(or daily), do you think that is necessary?

I am going to study for "Volatility Smile" later. It is an interesting subject to look into.

It is not useful to calculate Greeks weekly. Remember we are talking about the hedging strategy and effectiveness here instead of a trading P/L or a VaR position for a trading desk. Sure, one can calculate daily/weekly Greeks on the hedging portfolio, but it will be meaningful only if one can do weekly GMDB (underlying liability) valuation, which is not pratical.

Vol smile/smirk/frown have been somewhat well studied, but the correlations are not. Someone once suggested a "dynamic" or "stochastic" correlation matrix which would be of critial importance in Long Term Capital's case when unforeseen correlations emerged under certain extreme events. Have fun!

[WWSituation]

bump - this was good stuff.

[brauncj]

Let's say a company is pricing a VA GLWB rider that offers a reset and a 6% rollup. Said company does stochastic pricing using both real world and risk neutral pricing. My question is if the equity return in the real world scenario file has a long term average of 8% and the risk neutral file has a long term average equity return of 4% is the risk netral run going to overstate the cost of the rollup?

Now I understand that by using the real world expected return it changes the magnitude of the up and down moves in a binomial tree along with the probability of the up and down move. I guess my question really is if the 6% rollup has been set assuming that the equity markets return the risk-free rate plus a risk premium why wouldn't you make a risk premium adjustment to the rollup?

[campbell]

Hmmm, that argument reminds me of the public pensions argument(s) going on right now.

Just in case you didn't know this, Black-Scholes is a simplification of what we've actually seen equities do. Actual returns have "fatter tails" (see Taleb and his Black Swan book), and options are priced accordingly (thus, the volatility smile). And with the reset, you've got not only the left tail (i.e. bear market) but the right tail to worry about. If anything, I believe using a straight Black-Scholes risk-neutral pricing, without fattening up those tails, will understate the cost of the option.

VAGLBs can be very dangerous things. Too many guarantees are put in with people being blase' about how the volatility can kill a product.

[Eimon Gnome]

Hmmm, that argument reminds me of the public pensions argument(s) going on right now.

Just in case you didn't know this, Black-Scholes is a simplification of what we've actually seen equities do. Actual returns have "fatter tails" (see Taleb and his Black Swan book), and options are priced accordingly (thus, the volatility smile). And with the reset, you've got not only the left tail (i.e. bear market) but the right tail to worry about. If anything, I believe using a straight Black-Scholes risk-neutral pricing, without fattening up those tails, will understate the cost of the option.

VAGLBs can be very dangerous things. Too many guarantees are put in with people being blase' about how the volatility can kill a product.

Campbell speaks the truth.

Another cause of the smile is simple business economies. If you ran an equity trading desk and a guy wanted to buy a 20 year call on the S&P 500 @ 125% of current price and a $100m notional...well that's a tiny tiny price for a huge huge risk. I don't care that your formula says its worth 12 cents. There's a minimum amount I'm going to charge you for the bother of doing the paper work on the transaction, and then carrying that silly thing on my desk for 10 years while I wait for the tenor to come into the active trading market. Darn straight, you are going to pay a premium over that silly formula you've got. If you want the option, it's $25k, take it or leave it. I'm running a business here.

I guess I'm saying that it's dangerous to think of the vol in a BS formula as being the expected realized vol over the tenor of the option. There's more involved in the pricing than just log normal curves.

[JMO]

I guess I'm saying that it's dangerous to think of the vol in a BS formula as being the expected realized vol over the tenor of the option. There's more involved in the pricing than just log normal curves.

E.G. speaks the truth.

[campbell]

The reason B-S/lognormal model is used is because it's =easy=. It's easy to fit, and it's easy to calculate expected values and probabilities. And there is so much plug-and-play stuff based on B-S out there. So mental and financial costs to implement are low. The stochastic volatility models, and regime-switching models, are much more difficult to calibrate and require a lot of computing sometimes to get the numbers you want.

For the same reason, linear fits are used all the time for data when it's not particularly appropriate. If the point is to get a qualitative idea of what's going on, linear models can be good for exploratory work, just like B-S. But if one were implementing a full-fledged hedging program, I wouldn't just go with B-S. I would use it to develop some ideas in a quick & dirty manner, but for the practical execution, I'd need to do far more work in computing.

[kazh]

The reason B-S/lognormal model is used is because it's =easy=. It's easy to fit, and it's easy to calculate expected values and probabilities. And there is so much plug-and-play stuff based on B-S out there. So mental and financial costs to implement are low. The stochastic volatility models, and regime-switching models, are much more difficult to calibrate and require a lot of computing sometimes to get the numbers you want.

For the same reason, linear fits are used all the time for data when it's not particularly appropriate. If the point is to get a qualitative idea of what's going on, linear models can be good for exploratory work, just like B-S. But if one were implementing a full-fledged hedging program, I wouldn't just go with B-S. I would use it to develop some ideas in a quick & dirty manner, but for the practical execution, I'd need to do far more work in computing. :iatp: Lognormal models are inconsistent indicators of future values. Despite that, lognormal models are continually used. Ease of calculation seems the most plausible explanation for the popularity of poor models. :shrug:

[JMO]

:iatp: Lognormal models are inconsistent indicators of future values. Despite that, lognormal models are continually used. Ease of calculation seems the most plausible explanation for the popularity of poor models. :shrug:

Can you say Balducci hypothesis?

[JMO Fan]

I hear Millliman is developing a Stochastic Modeling Monograph for the International Actuarial Association. Does anybody know anything about this? Perhaps we have something to look forward to. :tup:

[California]

Until we get the Milliman report, here is a short summary (not related to Miliman per se). See page 9 for a discussion of B-S-M.

http://www.actuaries.org/CTTEES_FINRISKS/Documents/A_Note_on_Financial_Economics.pdf