バリアー・オプションの価値

「オプション道場」によってバリアオプションは「原資産の価格がある一定の価格を達するかによって有効になったり無効になったりが特徴」。　　The option is determined to be active or inactive based on whether or not the underlying stock price crosses a barrier. The types of such options include knock-in calls/puts and knock-out calls/puts. The relevant question I had was how pricing of these instruments differs from the pricing of vanilla options (which might be done via the Black-Scholes formula). The text "Black Scholes and Beyond" by Neil Chriss proposes that these options can be priced on a binomial tree. The tree is a standard Cox-Ross-Rubinstein tree with option nodes near the barrier stock price adjusted for the price of the "target security" (either a vanilla option if the barrier option knocks in or the rebate if it knocks out). Note that this is a tree which assumes a constant volatility for the underlying, not a tree which allows for "local volatility" (like an implied volatility tree or implied binomial tree).