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Insights
On this page, you will find a collection of articles curated by our financial experts.
These articles cover the most trending topics in the financial sector, providing valuable insights and analysis.
01
Arbitrage in the Perfect Volatility Surface
Dr. Uwe Wystup
Constructing the FX volatility surface is an ongoing challenge in the derivatives industry, even for quants – or should I say, only for quants, because I am quite sure the vast majority of the population couldn’t care less? Starting from at-the-money volatilities (ATM), risk reversals (RR) for 25- and 10-delta, butterflies (BF) or strangles for 25- and 10-delta, we need to find a smile curve, and taking term structure into account, a volatility surface that prices these quoted market instruments correctly and satisfy a number of conditions including but not limited to:
1. Smoothness, ideally up to second order: to construct a local volatility model;
2. Reasonable slope on the wings: to match prices of variance swaps;
3. Reasonably rich to reflect negative market strangle quotes;
4. Extendable to a consistent spreading logic;
5. Free of arbitrage
The smile construction interacts with the choice of interpolation and extrapolation. To explore the various methods & read the full article, please click here
02
How a Long Call Option can be Long, Gamma, Long Theta and Short Theta
Dr. Uwe Wystup
In my options training courses, I often ask participants if a long vanilla option can be both long gamma and long theta. Normally, options textbooks train us that the value of an option is the sum of its intrinsic value and the time value. As time progresses, the value converges to the payoff function, and the time value converges to zero. It is one of the common misconceptions that time value is always positive. If the forward curve goes down (backwardation), the time value can be negative for in-the-money options, i.e., the value of the call option is less than the payoff function. And in FX markets, this is quite common. As an example, we consider a market in USD–JPY, where USD interest rates are higher than JPY interest rates, and therefore the forward curve decreases. With a negative time value, we would then conclude that a deep in-the-money long USD call JPY put option is long gamma (because the payoff is convex) and long theta, because the value is below the payoff and converges up to the payoff. Today, we stretch this phenomenon a bit further and show that such a USD call can be short theta after all and will further learn that it can be both short theta and long theta. No kidding.
The market I consider is USD–JPY spot 127.00 on the trade day May 26, 2022, with spot date May 3, USD six-month money market interest rate 1.77%, JPY six-month money market interest rate -0.40% (yielding a six-month forward rate of 125.61 below initial spot), ATM volatility 9.634%, 25-delta risk reversal -0.654% (favouring USD puts), 25-delta butterfly 0.441% (standard).
To see a real example & access the full article, please click here
03
Why are USD-JPY Risk Reversals always Negative?
Dr. Uwe Wystup
As a typical currency pair with a negative Risk Reversal, I always pick USDJPY. Quite reliable. One might then wonder why USD-JPY Risk Reversals are always negative. Well, actually, that is not true. See the history in Figure 1. But almost, with some short periods of exceptions. In this column, I will explain the reason. A negative Risk Reversal means that out-of-the-money USD put JPY call options are priced at a higher volatility than USD call JPY put options: options with lower strike prices are more expensive than options with higher strike prices, causing a down-skew.
To access the full article to understand the Market Situation & The Impact of Power Reverse Dual Currency Bonds please click here