# Questions tagged [call]

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### Why is this inequality strict for arbitrage argument for European call?

in the notes about arbitrage arguments I am reading, I notice the statement We can also see that $$C^E_t>(S_t-K\mathrm{e}^{-r(T-t)})^+$$ Notice that the inequality holds STRICTLY! I don't ...
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### Can the Feynman-Kac formula be used for asset classes that don’t have options?

So rather than a call option C(S_t,t) we have some type of asset with asset price is given by S(x,t) where x is any type of variable that the asset price depends on. I.e Price of wooden desks, W(x,t) ...
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### How to apply the Spanning Formula (Carr-Madan) on European Call-option?

In the paper Optimal positioning in derivative securities (Carr & Madan, 2000) the so-called "Spanning Formula" for replicating payoffs is presented in section 2.1 as equation (1). It ...
1 vote
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### local volatility not reasonable

We are going to generate synthetic option prices using a Heston model, i.e., $$\begin{gather*} dS_t = \sqrt{v_t} S_t dZ_t,\\ dv_t = \lambda (\mu - v_t) d_t + \eta \sqrt{v_t} dW_t, \end{gather*}$$ ...
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### Pricing for basic option strategies [closed]

If I am trying to price a strategy, say for example a call spread where we are long a call, strike L and short a call strike M, would the pricing formula simply be the Black-Sholes price for the Call ...
1 vote
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### Deterministic optimal call time

Consider a American Option on a linear payoff i.e., if called at time $T$, it pays off $S(T)$, the stock price. Is the optimal call time of such an option determinsitc? Is there an intuition to the ...
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I have created a bull call spread. There was spread of 70 dollars between the option premium of 2 strikes I selected. Now the spread between option premium of 2 strikes is greater than 100 dollars. ...
The Black-Scholes price of a European call option is given by $$C_0^{BS}(T, K) = \mathbb{E}_Q[e^{-rT}(S_T - K)_+] = S_0 \Phi(d_1) - Ke^{-rT}\Phi(d_2) ,$$ where $$d_{1,2} = \frac{\log\big(\frac{S_0}{... 0 votes 0 answers 39 views ### VaR of protfolio with put and call I've stumbbled into this question in a job interview and didn't know how to answer it: Calculate the VaR of a portfolio where you are long put and long a call 7 votes 3 answers 1k views ### Which is riskier: a call option or the underlying? From Joshi's Quant Interview Questions and Answers: What is riskier: a call option or the underlying? (Consider a one day time horizon and compute which has bigger Delta as a fraction of value). I ... 1 vote 2 answers 138 views ### Failing to replicate Wilmott's results for binomial option pricing I am working through Paul Wilmott introduces Quantitative Finance, 2nd ed. I am failing to reproduce one of his numerical examples and I would like to understand why. I chapter 3, Wilmott introduces ... 5 votes 1 answer 145 views ### FX Call under stochastic rates and deterministic volatility Lets denote S_t, r^d_t,r^f_t respectively the FX spot, the domestic rate and the foreign rate at time t. Lets \mathbb{Q}^d , \mathbb{Q}^f respectively be the domestic and foreign mesures,... 1 vote 1 answer 56 views ### call vs average of prices Consider a two-period binomial model, with one risky asset. The are two types of options: call option with strike price K, i.e., the payoff is given by g(S_T)=(S_T-K)^{+} option with payoff given ... 0 votes 0 answers 95 views ### Geometric brownian motion and probabilities A stock's price movement is described by the equations dS_t=0.02S_tdt+0.25S_tdW_t and S_0=100. An investor buys a call option on said stock with a strike price K=95 which expires in T=2 years. ... 0 votes 1 answer 162 views ### Double Call Option A double call option allows the holder to either exercise at time T_{1} or time T_{2}, where T_{2}>T_{1}. With corresponding strike prices K_{1} and K_{2}, it can be shown that it is never ... 0 votes 1 answer 91 views ### Call Probability of European callable IRS When pricing a callable IRS (say only one call date) with a diffusion model (e.g. HW 1F) with a Montecarlo resolution, one can get the call probability on the call date versus maturing the date (which ... 1 vote 0 answers 60 views ### What is a call-spread and its formula? I am attempting Mark Joshi's The Concepts and Practice of Mathematical Finance. In B.3 Project 1: Vanilla options in a Black-Scholes world, he asked the following question. We need to be sure that ... -1 votes 1 answer 128 views ### 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 ... 1 vote 2 answers 136 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}}$$Is there an intuitive explanation for why this ... 0 votes 1 answer 62 views ### Graph of European call option value versus future price Given a standard European call option on a non-dividend-paying stock. Draw the graph of call price at time t versus the future price F(t,T). The future price F(t,T) is observed at time t, ... 3 votes 1 answer 238 views ### Boundaries for Call Spread I'm reading an interview book called A Practical Guide to Quantitative Finance Interview and I have some doubts regarding part of its solution and highlighted them in bold: Question: What are the ... 4 votes 1 answer 174 views ### Is the vega of a portfolio of a long 0.5 delta and short two 0.25 delta calls positive or negative? More specifically what I am trying to find out is whether the following relationship is always true or not. Same underlying for the calls, assume the most simplistic assumptions (interest rate = ... 1 vote 2 answers 125 views ### Why is higher the call price, the higher the price of a callable bond? I am preparing for FRM level 2, but I ran into a question whose answer was confusing to me: In the answer, it says "all other things remaining the same, the higher the call price, the higher the ... 1 vote 0 answers 61 views ### Binomial Model - completeness in presence of arbitrage Consider a uniperiodal binomial model where I buy one bond of value B_0 and rate r=0.1, and h stocks with price S_0=5. The value of the portfolio at time t=0 is$$ V_0 = B_0 + hS_0, $$... 2 votes 1 answer 287 views ### Risk Reversal quoting convention in FX market How is RR bid offer quoted in market? For example: If a 25delta call and 25delta put is quoted as 5.5%/5.6% and 5.3%/5.5% respectively. What would be quote of a 25d RR with these call and Put? 1 vote 1 answer 146 views ### European Call option replication An asset S_t is evolving according to the Black-Scholes model. We want to replicate a call option on this asset by holding Delta units of the asset at every time. I use a Monte Carlo algorithm to ... 1 vote 1 answer 593 views ### Calculate the price at time t=0 Assume the risk-free bond Bt and the stock St follow the dynamics of the Black & Scholes model (with interest rate r, stock drift \mu and volatility \sigma). Calculate the price at time t = ... 1 vote 0 answers 96 views ### Prove the following Call and Put relationship: [duplicate] I need to prove that$$c(S,X,T)=\frac{X}{F}p(S,\frac{F^2}{X},T)$$where$$F=Se^{(r-q)(T-t)}$$I am having trouble proving this relationship. Is this relationship even possible? If so, can someone ... 1 vote 1 answer 64 views ### Calculating the max. risk free interest rate with two given options I have an excercise where we have two European Call Options, which have the same underlying, same maturity t = 3, same interest. The only difference is their price and their strike. The price of the ... 1 vote 1 answer 266 views ### Interest rates, effect on call price Generally, we assume that an interest rate increase makes the call price more expensive. From my understanding it is because the expected return on the stock price increases. However the interest rate ... 3 votes 1 answer 2k views ### Delta Hedging/ Exchange for Currency Options I'm looking at 2 cases of hedging EURUSD, using call spread or range forward. Lets say spot is 1.1300 and my buy call is at 1.1300 and sell call is at 1.1500. Hypothetically I'm assuming that this is ... 2 votes 1 answer 482 views ### How to derive and interpret the duration of a call option? I read here that CFA students are taught that$$ D_{C} = \frac{\Delta_{C} D_{B} B}{C} $$Where D is the duration, \Delta_{C} is the first derivative of the options price with regards to the ... 4 votes 0 answers 169 views ### Zero-rebate barrier option pricing under the Heston model I'm trying to derive an approximation for the zero-rebate barrier option under the Heston model:$$dS_t=\mu S_tdt+\sqrt{v_t}S_tdW^S_tdv_t=\kappa(\bar{v}-v_t)dt+\eta\sqrt{v_t}dW^v_t,\quad d\langle ...
Im having a question about this standard derivation of the Black-Scholes formula: http://www.soarcorp.com/research/BS_hedging_portfolio.pdf The paper states $$C=\Delta S+B$$ and finally \$\Delta = ...