THE RIGHT INTERST RATE

One of the most frequent questions that comes up in options seminars is: What is the correct interest rate to use when calculating theoretical option prices and implied volatilities? The answer: Your interest rate.

If you bought options with money you would otherwise have put in three-month Treasury bills, then use the three-month T-bill rate. If you sold options short and your broker is paying you 2% on the resulting credit balance, use 2%. If you bought options with money you would have used to pay down your 7% mortgage, use 7%.

And if you bought those options with money you borrowed from Louie the Loan Shark at 240% interest (not recommended, by the way), then 240% is the correct number to use.

THE ASYMMETRY OF OPTIONS

It would seem logical that if the futures are at 112, a 113 call would be worth the same as a 111 put. After all, they’re both one point out-of-the-money. But in reality, the 113 call is worth more. That’s because your option pricing model takes into account the fact that the downside is limited — the underlying can only go down to zero — while the upside is theoretically infinite.

To understand, think of silver when it was trading at $5 an ounce. Which would you rather own, a $1 put, or a $9 call? Intuitively, you probably answered a $9 call, and you’d be right.

Statistically, it is “harder” for the price to go from $5 down to $1 than from $5 up to $9. A move from $5 to $4 is a 20% move. To get from $4 to $3 requires a 25% move, from $3 to $2, a 33% move, and from $2 to $1, a 50% move. Going from $5 to $6 also requires a 20% move, but from $6 to $7 only requires a 17% move, from $7 to $8, a 14% move, and from $8 to $9 just a 12.5% move.

That’s the basis of the asymmetrical “lognormal distribution” used in most option pricing models. It’s also the reason that if the underlying is at 112, the delta of a 112 call will be slightly above 0.5, and the delta of a 112 put will be slightly below 0.5.

SHORTING VOLATILITY

When you’re short premium (short volatility) — say that you sold short 50, 112 straddles with the underlying at 112 — then with every move in the underlying you lose money, your deltas move against you, and every time you buy or sell the underlying to return to delta neutral you’re locking in a loss. This is exactly the opposite of being long volatility.

The short-premium game is to keep your cool, and hope that each move of the underlying away from the strike price is temporary. If you can take the pain and refrain from evening up your deltas, and if the underlying does expire near your strike price, you will be handsomely rewarded. But if the underlying makes a big move…ouch!

Premium sellers make money more often than not because most of the time, nothing much happens in the markets. But when the markets get roiled and things move, losses can be huge.