# Questions tagged [call]

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### Cash-or-Nothing Call Option

I am trying to price a cash or nothing call option and I know know that the Cash or Nothing formula for a call option is $C(t,s)=Xe^{-r(T-t)}*N(d)$ If I have payoff X=100 r=0.03 T=2 $\sigma=0.3$ I ...
63 views

### Cash or Nothing Call Option using Binomial Method Matlab

I am trying to price a cash-or-nothing call option using the binomial method in Matlab. A cash or nothing call has payoffs $A$ if $S(t)>E$ $A/2$ if $S(t)=E$ $0$ if $S(t)<E$ The code I ...
76 views

### Deltas on Barrier options vs Vanilla options

In "Heard on the Street" it states that $$\Delta_{\text{up and out call}} \leq \Delta_{\text{standard call}} \leq \Delta_{\text{down and out call}}$$ Is there an intuitive explanation for why this ...
147 views

### Is the vega of a portfolio of a long 0.5 delta and short two 0.25 delta calls positive or negative?

More specifically what I am trying to find out is whether the following relationship is always true or not. Same underlying for the calls, assume the most simplistic assumptions (interest rate = ...
42 views

### Graph of European call option value versus future price

Given a standard European call option on a non-dividend-paying stock. Draw the graph of call price at time $t$ versus the future price $F(t,T)$. The future price $F(t,T)$ is observed at time $t$, ...
60 views

I'm reading an interview book called A Practical Guide to Quantitative Finance Interview and I have some doubts regarding part of its solution and highlighted them in bold: Question: What are the ...
1k views

### Value of Call Option as Volatility goes to Infinity

Why would the value of a call option go infinity as volatility goes to infinity? I understand how you could solve this question by taking $\sigma \rightarrow \infty$ in the solution to the black ...
71 views

### Why is higher the call price, the higher the price of a callable bond?

I am preparing for FRM level 2, but I ran into a question whose answer was confusing to me: In the answer, it says "all other things remaining the same, the higher the call price, the higher the ...
37 views

### Binomial Model - completeness in presence of arbitrage

Consider a uniperiodal binomial model where I buy one bond of value $B_0$ and rate $r=0.1$, and $h$ stocks with price $S_0=5$. The value of the portfolio at time $t=0$ is $$V_0 = B_0 + hS_0,$$ ...
74 views

### Risk Reversal quoting convention in FX market

How is RR bid offer quoted in market? For example: If a 25delta call and 25delta put is quoted as 5.5%/5.6% and 5.3%/5.5% respectively. What would be quote of a 25d RR with these call and Put?
63 views

### European Call option replication

An asset $S_t$ is evolving according to the Black-Scholes model. We want to replicate a call option on this asset by holding Delta units of the asset at every time. I use a Monte Carlo algorithm to ...
176 views

288 views

### Call option Delta

I have an exercise where I need to show that the prices of call options $C(t,K)=E((S_t-K)^+),t \in [0,T]$ with Strike $K$ for fixed $t$: $$\frac{\partial ^+C(t,K)}{\partial K}=-P(S_t>K).$$ We ...
93 views

### Black & Scholes with stochastic interest rate [duplicate]

Consider the following model $$\begin{cases} dS_t=r_tS_tdt+\sigma S_tdW_t, \\ dr_t=adt+\eta dW_t\\ \end{cases}$$ where $W$ is a Brownian motion and $\sigma, a ,b, \eta$ are positive constants. I ...
611 views

### Log-moneyness definition [closed]

Define the time-0 log-moneyness of a call on stock $S$ with strike $K$ and expiry $T$ to be: $$\log(S(0)\exp(rT)/K)$$ What does it mean for the strikes K to be at-the-log-moneyness?? I guessed this ...
284 views

### How to make the arbitrage if intrinsic value is greater than European call value

It always says if the intrinsic value is greater than European call value, there will be a arbitrage opportunity，but how to construct the portfolio $(S_t - K)^+$ or how to make this arbitrage. By the ...
331 views

### Black-Scholes European call price taking limits

Given that the Black-Scholes formula for a European Call is given by: $$C(S,t)=Se^{-D(T-t)}N(d_1)-Ke^{-r(T-t)}N(d_2)$$ $S$ is stock price, $K$ is strike price When I take limit as $t\rightarrow T^-$...
921 views

### Black-Scholes formula proof, without stochastic integration

I've looked into many books at my academic library, and very often it goes like this: Brownian motion Then, stochastic integration (Itô's formula etc.) Application: Black-Scholes formula for price of ...
78 views

### European call options and strikes [closed]

We consider 2 European call options with the same underlying asset, the same maturity date $T$ and with 2 different strikes $K_1$ and $K_2$ such that $K_1\leq K_2$. We denote $C^1_{0}$ and $C^{2}_{0}$ ...
815 views

### Put call parity in practice

I understand the Wikipedia article for put-call parity on a theoretical level: if you magically had portfolios consisting of 1) long a call, short a put, and 2) long the stock, short a discounted ...
103 views

### How does gamma trading depend on $K$?

If we think realized vol > implied vol, then we might go ahead and delta hedge a call, hoping that profits from gamma outweigh the decay. Question: What should $K$ be on the call? ATM? If so, why? ...
227 views

### Fair value for a LEPO (Low Exercise Price Options)

In one of my lecture notes, I stumble across this exercise question: Consider Low Exercise Price Options, LEPOs, (with dividends) in Australia. Using the value at the outset, explain why such ...
267 views

### How to price a call option which depends on two Wiener processes?

Could someone explain to me why the regular call pricing formula works, just with $\sigma$ replaced by $\|\sigma\|$ in the case where the underlying asset depends on two Wiener processes? For example,...
187 views

### When a stock's price could suddenly drop to zero before expire. does black-scholes misprice the option? Too high or Too low?

Quantitative Question – BLACK SCHOLES Consider a call option on a stock. Assume that Black-Scholes prices the option correctly if all of the assumptions of Black-Scholes hold true. Assume in addition ...
66 views

### how to understand the zero vol condition in Heston stochastic vol model

I can't understand one of the boundary conditions in Heston's model: $$c(t,s,0) = (s-e^{-r(T-t)}K)^+$$ Why the current vol is zero can deduce such result. here $c(t,s,v)$ $s$ is current price and $v$ ...