Managing an Option Portfolio around and Economic Events or Cooperate Action Dates

In the advent of Economic Events and Cooperate Action the following can happen:
• Implied volatility can increase leading up to the event and subsequently fall after directional move
• Implied volatility can increase leading up to the event and subsequently increase with the historic volatility also increasing

Depending on the event an option portfolio need to hedged as follows

If the even would result in the option volatility rising up to the then the following need to be checked:
• Is the volatility surface skewed towards the back months, in which case the option’s implied time to expiration should be compared using the forward options implied volatility and by fudging the time to expiration, if the fudged time to expirations are some what than they actually are, this can be used as a candidate for a diagonal spread
• Whether the event would be directional or would create uncertainty

If the event would create uncertainty the ideal position would be to make the portion of options (equity option if it is a cooperate event, equity and index related option if it is an economic event) which would be effected by such event Vega neutral but Volga positive, while being delta neutral. This can be done by going diagonally.

If the uncertainly reduces after the day with a possible large change in asset value, the ideal would be negative Vega.

Why buying out of the money options make sense in a market making perspective and volatility trading perspective

I was initially intrigued when I heard that Taleb was trading on out of the money option. In a way this makes sense since he has exposure to market making. I shall discuss below why this is a sensible strategy from two perspectives.

Market making perspective

In out of the money option pose lesser risk to a market maker than option this are either in or near the money. Since their delta is small, the market maker need not bring down his ask on a small unfavourable price move, but if the price move is large then the liquidity might dry up and might not be able to sell the out of the money option. Also due to liquidity of the options the market maker can lower his bid on them thus gaining a larger spread. Though a market maker need not lower his ask on a downward move he is in a position to increase the ask on a by a greater margin on an upward move. In extreme events the option inventory may end up in the money. The time decay of the options is also less or negligible when considering the market makers holding time.

Also the market maker can scalp using his inventory of out of the money option to make an additional amount of money. (If a trader has DMA then also he is in the position to make money by “juggling” an out of the money option portfolio.) All these do not require any predictive power in the market, which in deed is very difficult to do consistently.

If out of the money options are bought

Reference: http://www.cs.cmu.edu/~softagents/papers/CR_nevmyvaka_sycara_seppi.pdf

http://www.investorschronicle.co.uk/InvestmentGuides/Shares/article/20080423/eaf42688-f417-11dc-96a0-0015171400aa/Shares-Understanding-Level-2-market-makers--DMA.jsp

http://www.investorschronicle.co.uk/InvestmentGuides/default/article/20061124/443df720-e8ff-11db-9f1b-00144f2af8e8/Which-DMA-platform.jsp


Volatility Trading Perspective

dV / V = 1 / V * (∂V/∂S * dS + ∂V/∂σ * dσ + ∂V/∂T * dT + ∂V/∂r * dr)

E(ΔV / V) = 1 / V * Delta * E(ΔS) + 1 / V * Vega * E(Δσ) + 1 / V * Theta * ΔT + 1 / V * Rho * E(Δr)

E(ΔV / V) = Lambda * E(ΔS) + 1 / V * Vega * E(Δσ) + 1 / V * Theta * ΔT + 1 / V * Rho * E(Δr)

Returns can be maximized by buying the Option Greeks at the cheapest weighted by the expected change in the factor.

When trying to maximize the return by buying the Greeks cheap would mean that you end up buying somewhat out of the money.

Thing to watchout here is trasaction cost. This can eat all your profits.

Decomposing Option Price for Imperfections – Smile, Skew, “Abnormal” Distribution

Currently, it is very rare to see options trading at the Black Scholes price. The reason for this can be classified as:
* Market anticipation of future volatility
* Volatility of volatility effects (which results in the volatility skew or smile), and
“Imperfections” of actual returns distribution

All these are fitted into the fitting parameter which is volatility.

In identifying underpriced options, the above effects should be removed from the implied volatility and residual volatility should be compared with the historic volatility. When doing this, things to consider is that the effects of vvol is not present for ATM options, thus, theirs price reflects more of anticipatory and adjustments for the distributions imperfections.

Imperfections in the distribution results in the distribution’s moments diverting from the normal distribution. These can be modeled using moment fitting techniques where one option is decomposed into a basket of BSOPM options at different vols. The de composition can take the following form:
* Fit a kernel to the distribution and get the basket for the imperfection effects plus the normal BSOPM effects
* Subtract the BSOPM priced option to get a zero weight basket which has the pure imperfection effects
* From the observed price of an ATM option subtract the above to get the price component of the anticipator vol. effects
* The deference between the ATM and options at the other strike with the same term is the risk of volatility effect

NB: in a basket all the option parameters should reflect the modeled option except for the implied volatility which is the fitting parameter.

Best regards, Suminda Sirinath Salpitikorala Dharmasena

Open Thoughts on Finance

A long position’s expected returns are path dependent since it can be sold off. A writer’s position is not so in the absence of dynamic hedging.

Implied volatility is a function volatility at the money and vol + vvol + v2vol + … at other strikes.

Black Scholes Option Pricing

Since BS is widely recognized and established, largely it is worthwhile to look into implied volatility fudges to accommodate various “imperfections”. This would be ideally suited if the model is to interpreted by humans. If it is pure algo, other methods can be used but also displaying the BS implied vol deviations. The read thing about it is that it has only a few parameters to estimate thus easily comprehendible by the human users.

I have being thinking about this for some time but reading the following post by Paul Wilmott made me accept it to a great extent: http://www.wilmott.com/blogs/paul/index.cfm/2008/4/29/Science-in-Finance-IX-In-defence-of-Black-Scholes-and-Merton

Suminda Sirinath Salpitikorala Dharmasena

Utility of a Derivative in the Presence of Secondary Markets and Without Secondary Markets

The utility of any instrument would be different when there are secondary markets. The valuation of such instruments should take this into account!

With regard to option pricing models, I feel the model only shows the utility of the parties for over the counter markets. Options can be sold and bought back in the secondary market.

If this was not the case and the buyer is compelled to hold it to expiration or exercise, then the payoffs can be modeled using a replicating portfolio.

Please be good enough to comment on this.

Best regards, Suminda Sirinath Salpitikorala Dharmasena