Do Properly Anticipated Prices Fluctuate Randomly? Evidence from VIX Futures Markets

According to Marketwatch, Goldman Sachs strategists just issued a warning regarding the volatility index, VIX,

Goldman analysts Rocky Fishman and John Marshall said that the VIX, which uses options bets on the S&P 500 to reflect expected volatility over the coming 30 days, has been hovering at or below 13, marking its lowest level since around January (though it is tipping up in Monday trade). Its current level takes the gauge of implied volatility, which tends to rise when stocks fall and vice versa, well below its historic average at about 19.5 since the fear index ripped higher in February.

Goldman argues that the 5-day intraday swings of the S&P 500 have been out of whack with the price of the cost of a one-month straddle on the index. A straddle is an options bet that allows an investor to profit from a sharp move in an asset, but without wagering on the specific direction of that expected move. In other words, it is an inherent bet on volatility. A straddle can be structured by buying a put option, which confers the owner the right but not the obligation to sell an asset at a given time and price, and a call option, which offers the comparable right to buy an underlying asset, at the same expiration date and strike price. Read more

Volatility Index VIX as of May 18 2018

But is the volatility index predictable? How about VIX futures and ETFs?

A recent research article raised some interesting questions,

The VIX index is not traded on the spot market. Hence, in contrast to other futures markets, the VIX futures contract and spot index are not linked by a no-arbitrage condition. We examine (a) whether predictability in the VIX index carries over to the futures market, and (b) whether there is independent time series predictability in VIX futures prices.

The answer is no.

The answer to both questions is no. Samuelson (1965) was right: VIX futures prices properly anticipate predictability in volatility, and are themselves unpredictable. Read more

But then why do we trade VIX futures and ETFs?

We think that the reasons might be:

• Trading the spot VIX is difficult,
• When trading VIX futures and ETFs, we exchange the predictability of the spot index for a little extra return stemming from the volatility risk premium.

ByMarketNews

Overnight Index Swap Discounting

The overnight index swap (OIS) has come into the spotlight recently, due to the widening of the Libor-OIS spread. For example, the Economist recently reported:

WATCHING financial markets can be like watching a horror film. A character walks into the darkness alone. A floorboard creaks. The latest spooky sign is the spread between the three-month dollar London interbank offered rate (LIBOR) and the overnight index swap (OIS) rate. It usually hovers at around 0.1%, but has recently climbed to 0.6% (see chart). As it widens, bankers are bracing for a jump scare.

To see why, consider what each rate represents. LIBOR is the rate that banks charge other banks for unsecured loans. The OIS rate measures expectations for the federal funds rate, which is set by the central bank. As LIBOR rises above the OIS rate, that suggests banks fear it is getting riskier to lend to each other. (The gap was 3.65 percentage points in the depths of the crisis, after Lehman Brothers filed for bankruptcy.) Read more

[caption id="attachment_459" align="aligncenter" width="628"] Libor-OIS spread as at May 2, 2018. Source: Bloomberg[/caption]

What exactly is an overnight index swap?

An overnight index swap is a fixed/floating interest rate swap that involves the exchange of the overnight rate compounded over a specified term and a fixed rate. The floating leg of the swap is related to an index of an overnight reference rate, for example Canadian Overnight Repo Rate Average (CORRA) in Canada or Fed Funds rate in the US.

Usually, for swaps with maturities of 1 year or less there is only one payment. Beyond the tenor of 1 year, there are multiple payments at regular intervals. At the inception of the swap, the par swap rate makes the value of swap zero. That is, the net present value (NPV) of the fixed leg equals the NPV of the floating leg,

where N denotes the notional amount of the swap,

R_i-1,i is the forward OIS rate,

Z_i is the discount factor at time t_i

is the daily accrual factor, and

 s_K is the par swap rate of a swap with maturity t_K.

The OIS discount factors (DF) are often used to value interest rate derivatives that require a posting of collateral.  The OIS discount factor curve is built by bootstrapping from the short maturity and long maturity overnight index swap rates in order of increasing maturity.  The processes for backing out the discount factors from the short and long maturity swap rates are, however, different.

In the short end of the curve, given that there is only 1 payment, the discount factor is calculated based on the spot rates. At the long end of the curve, the DF curve is determined as follows,

• Payment dates are generated at each 6 months (or a year, depending on the currency) from the time zero up to 30 years,
• Par swap rates are determined at each payment date. To obtain the par swap rates for the payment dates where there are no swap quotes, one linearly interpolates the par swap rates in order to complete the long end of the swap curve,
• Using the par swap rates at each payment date, discount factors are obtained by solving a recursive equation.

This is just an introduction to OIS discounting. The process for building an OIS discount curve involves many technical details. We are happy to answer your questions.

Post Source Here: Overnight Index Swap Discounting

Can a Horse Racing System be Applied to the Stock Markets?

Bill Benter is one of the most profitable professional gamblers in the world. According to Wikipedia

William Benter was born and raised in Pittsburgh, Pennsylvania.[2] As he grew up, he wanted to use his mathematical talents to make a profit so immediately after finishing a university physics degree in 1977,[3] he went to the blackjack tables in Las Vegas and used his skills to count cards. He came across the book, Beat the Dealer, by Edward O. Thorp, which helped him improve his methods.[4] Seven years later, he was banned from most of Vegas’ strip’s casinos.[2]

Benter then met with Alan Woods, a like-minded gambler whose expertise in horse racing complemented his own in computers. The two became racing partners and in 1984, moved to Hong Kong.[3] Starting with a mere US$150,000 (equivalent to US$353,331 in 2017), the pair relied on their mathematical skill to create a formula for choosing race winners.[2]

Using his statistical model, Benter identified factors that could lead to successful race predictions. He found that some came out as more important than others.[5] Benter later worked with Robert Moore.

Benter is a visiting professor at the Southampton Management School[6] as part of the Centre for Risk Research and a fellow of the Royal Statistical Society.[7]

Bloomberg recently published an interesting story about his career, 

Benter grew up in a Pittsburgh idyll called Pleasant Hills. He was a diligent student and an Eagle Scout, and he began to study physics in college. His parents had always given him freedom—on vacations, he’d hitchhiked across Europe to Egypt and driven through Russia—and in 1979, at age 22, he put their faith to the test. He left school, boarded a Greyhound bus, and went to play cards in Las Vegas.

Benter had been enraptured by Beat the Dealer, a 1962 book by math professor Edward Thorp that describes how to overcome the house’s advantage in blackjack. Thorp is credited with inventing the system known as card counting: Keep track of the number of high cards dealt, then bet big when it’s likely that high cards are about to fall. It takes concentration, and lots of hands, to turn a tiny advantage into a profit, but it works.

Thorp’s book was a beacon for shy young men with a gift for mathematics and a yearning for a more interesting life. When Benter got to Las Vegas, he worked at a 7-Eleven for $3 an hour and took his wages to budget casinos. The Western—with its dollar cocktails and shabby patrons getting drunk at 10 a.m.—and the faded El Cortez were his turf. He didn’t mind the scruff. It thrilled him to see scientific principles play out in real life, and he liked the hedonistic city’s eccentric characters. It was the era of peak disco, with Donna Summer and Chic’s Le Freak all over the radio. On a good day, Benter might win only about $40, but he’d found his métier—and some new friends. Fellow Thorp acolytes were easy to spot on casino floors, tending to be conspicuously focused and sober. Like them, Benter was a complete nerd. He had a small beard, wore tweedy jackets, and talked a lot about probability theory. Read more

But can a winning horse racing system be applied to the stock markets? Benter himself provided an answer in this video

ByMarketNews