Derivatives on Thetabruv

Futures

Mon, 01 Jan 0001 00:00:00 +0000

Futures#

The future is the simplest derivative there is: a mutual commitment to exchange the underlying (or its cash value) at a future date, at a price fixed today. No premium to pay, no choice to exercise: just a symmetric obligation. Whoever is long gains if the price rises and loses if it falls; whoever is short, the exact opposite, dollar for dollar. It is the linear instrument of this site’s strategies, and it plays two roles: in the DHCS strategy (DHCS page) it is the delta-hedging instrument; in the TRPS (TRPS page) it is the night sentinel — the hook on which the bot’s overnight watch is armed and, in the last resort, plan B for emergencies — being the only index derivative that trades almost 24 hours a day.

Options

Mon, 01 Jan 0001 00:00:00 +0000

Options#

If the future is an obligation, the option is a right. Whoever buys a call acquires the right, not the obligation, to buy the underlying at a predetermined price (the strike) by or on a certain date (the expiry). Whoever buys a put acquires the right to sell on the same terms. Whoever sells the option (the writer) collects a premium upfront and takes on the mirror-image obligation: to suffer exercise whenever it suits the buyer. The asymmetry is all here: the buyer can lose at most the premium, the seller can lose far more. This page builds the minimum vocabulary needed to handle that asymmetry; the next one (Volatility risk premium) will explain why, on average, it is paid more than it should be.

Volatility risk premium

Mon, 01 Jan 0001 00:00:00 +0000

Volatility risk premium#

Here we are at the protagonist. The volatility risk premium (VRP) is the systematic gap between the volatility implied in option prices and the volatility the underlying then actually realizes. In the language of the Derivatives page: it is the distance between the Q world and the P world, measured on variance. In the insurer’s language: it is the difference between the premium collected and the average claim paid out. If it is positive and persistent, selling options is a trade with positive expectancy. This page gathers the evidence, explains the causes and — above all — makes clear exactly what the premium is the price of.

Capital efficiency

Mon, 01 Jan 0001 00:00:00 +0000

Capital efficiency#

We have established that the VRP exists (Volatility risk premium page). The next question is how much it pays, and here comes the first cold shower: in absolute terms, little. A deep OTM 1DTE put sells for about 15 cents, that is, $15 per contract. Repeated 252 times a year on a notional of roughly $730,000 (one SPX contract with the index at 7,300), that makes 15 × 252 / 730,000 ≈ 0.5% per year on notional. Half a percentage point. If collecting it required parking the entire notional in cash, the game would not be worth the candle: a T-bill pays more with no tail risk. The entire viability of volatility selling therefore hinges on a seemingly bookkeeping question: how much capital is actually needed to support the position. This is the subject of capital efficiency, and it is the point where many forum discussions go off the rails.