# Tag Info

16

A synthetic model for the VIX would be quite useful. I just mention this since it has been covered elsewhere in the past, although I don't think that it's a real solution to your problem (for a number of reasons). Several blogs posted on the "William's VIX Fix" (WVF) in the past: marketsci, trading the odds, mindmoneymarkets. The WVF is intended to be a ...

11

I haven't read Natenberg but it of course depends on your side in the trade: Are you a market maker or a risk taker? So do you live on the spread (first) or are trying to make money based on e.g. forecasts on direction (second). This is the great divide in QuantFinance! Only in the first case will all your option trades be delta neutral. There is a nice ...

7

5

The delta factor you seek is the spot to futures price ratio without having to use all those parameters. Now to answer your actual question: Since you are getting futures data, you presumably have the tickers. You can infer the expiration date from the ticker. Expiration dates are always on the third Friday of the month, and the ticker contains four ...

5

Well - if you're not delta neutral - this means you take a position with certain view on the market. This can be very comfortably done when you think that a stock price will go high up, but you don't want to spend all your money on acquiring the stock - you buy a call on it, which is quite cheap, and get the same payoff.

4

One other consideration is the cost of the trade. If you're not delta-neutral, you're expressing a directional view, and there are cheaper ways to express a direction view than options. (Namely, just owning the underlying.) So, conceptually, it's a little easier to think of there being two separate trades going on: an expensive vol trade (the options) and a ...

3

Judging by the math in a paper by Vahamaa (1999), you should measure the slope using the options closest to the strike you are examining. In other words, suppose that you are trying to come up with the skew-adjusted delta of an SPY option with strike of 130. Then the skew slope should be based on the 129 and 131 strike options. If these points happen to ...

3

Tangurena's answer and links give the right idea. You can get a rough approximation by finding the conversion price $K$ and using that $K$ as the strike in a standard Black-Scholes option pricer. In practice, most people work with 3rd party models such as the ones built into Bloomberg, Monis, or Kynex.

3

to match the constant 30-day VIX horizon, I think you would want to trade two straddles in the first and second expiration cycles and delta hedge, gradually rolling the weight towards the second month straddle and then finally to a new straddle at/near expiration each month. Here are some problems I can imagine for this approximation. Hedging error - the ...

2

One final thought: you want something that depends on volatility, but not on price. In other words, if SPX goes up, your VIX replicant wouldn't necessarily change at all. Would an SPX option calendar spread behave something like this, since option prices change w/ volatility, and short-term options change more than long-term options?

2

As I recall, Natenberg recommends selling time premium and places himself in the market maker camp that @vonjd describes. You are correct in noting that delta neutral holds for small changes in the underlying price. You can probably imagine a case where you sell a lot of deep out-of-the-money puts and sell a few slightly out-of-the-money calls. This would ...

2

Your portfolio composition is not clear. To simplify, we assume that it consists of units of a stock and options on this stock. What you can do is to sell 4000 units of options that will bring it to gamma neutral, and then to balance the delta, you can buy 2,400-450=1,950 units of the stock.

1

let $\frac{\partial C}{\partial S}=\delta_c$ let $\frac{\partial^2 C}{\partial S^2}=\Gamma_c$ let $\frac{\partial C_0}{\partial S}=\delta_0$ let $\frac{\partial^2 C_0}{\partial S^2}=\Gamma_0$ we want $\frac{\partial V}{\partial S}=\frac{\partial C}{\partial S}=\delta_c$ and $\frac{\partial^2 V}{\partial S^2}=\frac{\partial^2 C}{\partial S^2}=\Gamma_c$ ...

1

Lets give it a rough go then. Two assumptions. (1) We disregard repo (to lend the stock you may want to short) or financing on your hedged position. And (2) We assume no trading of the gamma on the option. Then I would assume the break-even is equal to the expiry should be equal to... (CALL) paidPremium/(1-hedgedDelta) + callStrike (PUT) putStrike - ...

1

There is a relationship: $\log \delta^{-1} = \frac{\sqrt{Var[r(t)]}}{\sqrt{p(1-p)}}$ Which relates the jump size to the volatility of short rate and risk neutral jump probability. The vol of short rate is chosen to be const in basic model, could be time-varying, but makes things complicated. To solve for $\delta$ you do need the vol of short rate given ...

1

Not sure this helps, but visit: http://delayedquotes.cboe.com/new/options/options_chain.html?symbol=SPX&ID_NOTATION=8941848&ID_OSI=10614550&ASSET_CLASS=IND and click on any option to see its Greeks.

1

the true way to replicate the vix is to use an infinite strip of out of the money calls and puts and actually, this is the definition of vix. it is $\sqrt{\int^{T+\Delta}_T v_s ds}$ where $v_s$ is realized variance. Peter Carr showed that we can value any exotic payoff, free of any option model by using the spanning formula. Let $g(S_T)$ be the exotic ...

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