- Non-linear payout means volatility matters to what the option costs: even though the distribution of future returns may be symmetric, option is worth something because it either goes to zero or +ve.
- Black-Scholes is the first step in quantifying what the value the asymmetry gives the option. Clearly, more vol means option is worth more. But also all the other Greeks fall out of it and are intuitive: theta accelerates towards expiration, interest rate/div moves the price, etc.
- When you're trading an option, you're trading the vol. All other numbers (rate/div/time/current price) are fixed, vol is the only degree of freedom.
- If you're long a call, you can sell some underlying to give your profit-vs-price graph a nice bowl shape. Same if you're long a put, you can just buy some underlying and whatever the market does, you will make money. When the market moves up, you make money. When it goes down, you make money. Now and again when you've made some money, you flatten your delta (sell high, buy low) and you're back at the bottom of a new bowl, and you can keep locking in gains. This is called being long gamma.
- Sounds nice, doesn't it? What's the downside? As time passes, the option loses value because there's less time for it to move a lot. If you don't manage to buy low and sell high enough to lock in the price of the option, you've net lost money.
- So what determines whether you will be able to do this trick, or perhaps the opposite (sell options and hope not to lock in losses)? The relationship between the implied volatility the option was bought for and the actual volatility that happened over the time that you had it.
- Non-linear payout means volatility matters to what the option costs: even though the distribution of future returns may be symmetric, option is worth something because it either goes to zero or +ve.
- Black-Scholes is the first step in quantifying what the value the asymmetry gives the option. Clearly, more vol means option is worth more. But also all the other Greeks fall out of it and are intuitive: theta accelerates towards expiration, interest rate/div moves the price, etc.
- When you're trading an option, you're trading the vol. All other numbers (rate/div/time/current price) are fixed, vol is the only degree of freedom.
- If you're long a call, you can sell some underlying to give your profit-vs-price graph a nice bowl shape. Same if you're long a put, you can just buy some underlying and whatever the market does, you will make money. When the market moves up, you make money. When it goes down, you make money. Now and again when you've made some money, you flatten your delta (sell high, buy low) and you're back at the bottom of a new bowl, and you can keep locking in gains. This is called being long gamma.
- Sounds nice, doesn't it? What's the downside? As time passes, the option loses value because there's less time for it to move a lot. If you don't manage to buy low and sell high enough to lock in the price of the option, you've net lost money.
- So what determines whether you will be able to do this trick, or perhaps the opposite (sell options and hope not to lock in losses)? The relationship between the implied volatility the option was bought for and the actual volatility that happened over the time that you had it.
The standard books on this:
Natenberg Hull Wilmott