Mirror options let investors change their view of the direction of the underlying stock, but without additional transaction costs. Get a pricing spreadsheet here.
Manzano (2001) developed Mirror options as a tool for investors to enage in greater speculative risk. They let investors call the market direction, but alleviates the burden of frequent transaction costs.
With this unique financial instrument, you can turn upward price swings into downward price swings, and vice-versa, at a date chosen by the option holder. The payoff at maturity is based on the reflected price.
The full mathematical detail can be found here
Mirror options have two flavours; long (with a positive payoff f) and short (with a negative payoff -f). However, given the nature of the option, holding both a long mirror call and long mirror put (with the same strike) is not the same as a straddle. This trading position has some value.
Mirror options have yet to gain traction in the financial markets, but promise greater speculative flexibility.
This Excel spreadsheet prices European Mirror options (including long/short calls and puts). The equations were sourced from this reference.