Hi everyone, just curious about this part. I thought that a higher volatility increases the price of the option? meaning if you overestimate the vol of an option, you would have overpriced options, rather than underpriced?
Hi @SyroneDavid Very good observation. Our summary picked it this up from the source (see below; emphasis mine). You are totally correct: option price increases with implied volatility; aka, percentage (long per-option) vega is always positive. The fact that these are interest rate options should not change that fact. Often times, there is a directional confusion (e.g., using ATM implied vol via BSM when there is a implied vol smile will "underprice" the option ...) but I do not perceive that to apply in this situation. While it seems possible the language is imprecise (I suspect the issue relates to the fact that, apparently, they were short option positions as the premium was overestimated), in my opinion, it does not change your observation: it appears to me to be a mistake in the reading. Thanks,
"Real OpRisk Events: Model Inputs Fraud, NatWest, March 1997 One of the most famous case in derivatives mispricing was the one that happened at NatWest in 1997. On February 28, 1997, a few days after the bank released its annual results, it announced a loss of approximately USD 150 million caused by a junior trader who has already left the bank. The trader was said to be dealing in long-dated OTC interest rate options, used by companies that borrow at a floating rate and purchase a cap on the interest payments. The major problem in valuing these options is that they are relatively illiquid. The trader calculated the price of the options by providing his own estimates of volatility, which he apparently overestimated, creating fictitious profits that built up in the books over time.
The volatility estimates resulted in the options being underpriced. The trader attracted more clients, booking the requested premium, thereby increasing the apparent profitability of his desk (and, by extension, his remuneration). The loss was realized
when the options were exercised." -- Marcelo G. Cruz, Gareth W. Peters and Pavel V. Shevchenko, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk (Hoboken, NJ: John Wiley & Sons, 2015). Chapter 2: OpRisk Data and Governance