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Questions tagged [call]

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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 ...
130 views

275 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 ...
89 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 ...
493 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 ...
247 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 ...
298 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 $t\rightarrow T^-$...
853 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 ...
76 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 $C^{2}_{0}$ ...
691 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 ...
100 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? ...
199 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 ...
244 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,...
182 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 ...
62 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 $v$ ...
4k views

why is the delta of a short call option negative? [closed]

Why is the delta of a short call option negative? In Black-Scholes-Merton equation the delta of a call option is always a probability function therefore it does not imply such a consequence. How do I ...
379 views

Equivalent form of Black-Scholes Equation (to transform to heat equation)

I am trying to understand the transformation of the Black-Scholes equation to the one-dimensional heat equation from Joshi, M. (2011). The Concepts and practice of mathematical finance. 2nd ed. ...
222 views

Callable Bond = long Bond - call on bond?

Can someone verify (maybe there is some literature around) the following relationships? Callable Bond= Long on Bond + short on a Call Position --> PV(CallableBond) = PV(Bond) - Call on Bond? or ...
The stock and bond under the Black-Scholes framework, no dividends: $$S_t=S_0e^{\sigma W_t+\mu t}=S_0e^{\sigma \tilde{W}_t +(r-\frac{1}{2}\sigma^2)t}$$ $$B_t=e^{rt}$$ where $\tilde{W}_t$ is $\mathbb{Q}... 2answers 1k views How many monte carlo runs do I need for pricing a Call? I have to price several calls using Monte Carlo. Obviously, there is a huge tradeoff between the number of runs and the fair price of the call option. I know I can check how the approximation changes ... 2answers 177 views How do you calculate price of non-existant call option on commodity future I've been stumped on this for awhile now. I'm trying to determine the price of a call option on a commodity futures contract that expires in the future. My issue is that while the future's contracts ... 1answer 100 views Qualitative properties of call I have read somewhere that we can show by using arbitrage argument the following relationship for call option : $$\frac{\partial{C_t(T,K)}}{\partial{K}}\leq0$$$$\frac{\partial^2{C_t(T,K)}}{\... 2answers 834 views Calculating Greeks in Covered Calls? Just want to confirm whether Delta, Gamma, Theta, Vega will be calculated in the following way? Since we own 100 shares of stock while selling a call we need to subtract greek value from one? right? ... 1answer 105 views Put call parity: when are the premiums the same? Please explain why put call parity could be compared to the payoff of a long forward contract. ie.$C_E-P_E=V_X(0)$where$C_E,P_E$are the call/put premiums and$V_X(0)$is the value of a long ... 3answers 55 views buy asset after exercising call options Suppose that I buy a call option at \$10 for a stock $S_0 = \$100$,$K = \$110$, expiry date $T$. In $T$, $S_T = \$140$, so that I exercise the option to buy and then sell the assets (buy at$\$110$ ...
I want to estimate delta, vega and gamma for a basket option. This option is a European Call option. The underlying is $S=\omega_1 S_1 +\omega_2 S_2$ Where: $S1$ = stock price of asset 1 $S2$ = ...