# Price of a Cash-or-nothing binary call option

## Cash or nothing option wiki

a. is correct, but you should derive it using appropriate logic, not just guessing the answer. Ie the drift of discounted stock should be 5. Define a bond dB = rBdt. d(S/B) should have no drift. This can help you find the correct mu. You can find the sde for S/B using two dimensional ito

## 3Black???Scholes for cash-or-nothing options - T??i li

Of course, this is not the complete list of binary option types. For instance, there are 78 different types of binary barrier options which exist both “cash-or-nothing” and “asset-or-nothing 8776 . Some of them will be covered in the next article.

### Binary Option - TU Wien

Interest-rate term structure (annualized and continuously compounded), specified by the RateSpec obtained from intenvset . For information on the interest-rate specification, see intenvset .

#### Determine price of cash-or-nothing digital options using

Settlement or trade date for the basket option, specified as an NINST -by- 6 vector of serial date numbers or date character vectors.

##### Digital Option Cash Or Nothing - Rendite Einer Anleihe

Price = cashbyls( RateSpec , StockSpec , Settle , Maturity , OptSpec , Strike , Payoff ) computes the price for cash-or-nothing European digital options using the Black-Scholes option pricing model.

c) Assume no yield anymore. Now, there is a derivative written on this stock paying one unit of cash if the stock price is above the strike price $K$ at maturity time $T$, and 5 else ( cash-or-nothing binary call option ). Find the PDE followed by the price of this derivative. Write the appropriate boundary conditions.

stockspec handles several types of underlying assets. For example, for physical commodities the price is , the volatility is , and the convenience yield is .

c. In this case the pde is the same as the black scholes pde using your risk neutral process. Can you think of why this is? Does the type of call option change how the underlying changes? What are the other boundary conditions ie (for S = 5 and S = infinity). Take a look at dirichlet (also known as zero gamma condition) and other types of boundary conditions.

For part (d), instead of using Girsanov's theorem as phubaba suggested, I believe that we can state directly that the price is $$V_t = e^{-r(T-t)} \mathbb{E}^Q \left[ u(S_T-K) \middle \vert \mathcal{F}_t \right],$$ where $u$ is the step function, $Q$ is the risk-neutral probability measure, and $\mathcal{F}_t$ is the filtration at time $t$, since the value of any European-style option with a payoff $f(S_T)$ is given by $V_t = e^{-r(T-t)} \mathbb{E}^Q \left[ f(S_T) \middle \vert \mathcal{F}_t \right]$.