# Questions tagged [call]

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### 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 ...
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The price of a call with a stock with Bachellier process as its underlying and zero interest rate is giving by: $$C(t)=(S(t)-K)\Phi(\frac{S(t)-K}{\sigma \sqrt{T-t}})+\sigma \sqrt{T-t} \phi(\frac{S(t)-... 1answer 144 views ### Question about the process of monte carlo simulation I have encountered an interesting question. Is it better to simulate the geometric brownian motion process for call itself or GBM for the underlying. My question is can we actually apply GBM to call? ... 1answer 161 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 ... 1answer 5k views ### Use of cash delta vs forward delta and the mirror image rule There has been no mention in this text of why this formula uses forward delta not cash delta. Why should have this been obvious to the reader? How can a put be delta neutral at 30%, what does this ... 2answers 222 views ### Analysis of exercising a call option early Most options traders sell their call options early instead of exercising them, as you would make a bigger profit this way due to being able to salvage some remaining extrinsic value. For example: ... 1answer 209 views ### Where do Over-allotment (Greenshoe) option shares come from? I'm just wondering, if following an IPO the share price goes up and the underwriter calls the option, where do those extra 15% shares come from? Does the company have to issue more stock to cover the ... 1answer 54 views ### What is the strike of a short put that mimics a covered call If I am long a stock X which I purchased at \100 and sold a covered call in the front month with strike \105 for \2 then is it true that the covered call is equivalent to a naked put at ... 1answer 105 views ### Call spread hedge I'm trying to understand how a call spread is used for FX hedging. The example that my book gives is when we have USD receivables in 12 months which we want to convert to EUR and we want to hedge ... 1answer 102 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 ... 1answer 239 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 ... 2answers 196 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 ... 2answers 1k views ### How to price an European call on zero-coupon from the yield curve? It is known that the price of an European call of maturity T^* on zero-coupon of maturity T is given by$$p(0,T)= B(0,T^*)\mathbb E ^{\mathbb Q_{T^*}}\left[ (B(T^*,T)-K)^+\right]$$where B(0,T)... 2answers 97 views ### Derivation for call option upper bound In Euan Sinclair's book, Option Trading, he writes that c <= S, the price of a European call must be lower than the price of the underlying stock. To prove it, he applies the principle of no ... 0answers 104 views ### Heston Model Calibration with MatLab: model prices do not fall in the bid-ask range I am currently implementing the MatLab code reported below for the calibration of Heston Model. The code seems fine and, by reading the paper where I took the code, I was able to calibrate and price ... 0answers 40 views ### What is a call-spread and its formula? I am attempting Mark Joshi's The Concepts and Practice of Mathematical Finance. In B.3 Project 1: Vanilla options in a Black-Scholes world, he asked the following question. We need to be sure that ... 0answers 53 views ### Binomial Model - completeness in presence of arbitrage Consider a uniperiodal binomial model where I buy one bond of value B_0 and rate r=0.1, and h stocks with price S_0=5. The value of the portfolio at time t=0 is$$ V_0 = B_0 + hS_0, $$... 0answers 80 views ### Prove the following Call and Put relationship: [duplicate] I need to prove that$$c(S,X,T)=\frac{X}{F}p(S,\frac{F^2}{X},T)$$where$$F=Se^{(r-q)(T-t)}$$I am having trouble proving this relationship. Is this relationship even possible? If so, can someone ... 0answers 486 views ### Black Scholes Replicating Portfolio Riskfree Asset Im having a question about this standard derivation of the Black-Scholes formula: http://www.soarcorp.com/research/BS_hedging_portfolio.pdf The paper states$$C=\Delta S+B$$and finally \Delta = ... 0answers 117 views ### Black & Scholes with stochastic interest rate [duplicate] Consider the following model$$\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 ... 0answers 82 views ### Delta of an option in two cases Let C be the prime of a call in fi=unction of the price in term F, Strike K, volatilité \sigma and maturity t: C(F,K,\sigma,t,r)  We assume that we know \delta \delta=\frac{\partial}{\... 0answers 167 views ### Volatility Skew for Put and Call options [closed] Given that the implied volatility follows volatility skew, which one has higher implied volatility? At-the-money put 40 (spot = strike = 40) or at-the-money call 160 (spot = strike = 160)? I am not ... 3answers 58 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 ... 1answer 56 views ### How are the greeks defined for the two legs or more strategies with regards to options? I am to figure out something, and can't find any reference. I wonder: does it make sense to talk of a delta or other greek of a strategy? It seems that you can't put a price exactly on a call spread ... 1answer 50 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, ... 1answer 226 views ### Decreasing value of the Put option with increasing Time to maturity [closed] Can you think of a situation when increasing the time to maturity lowers the value of a put option? If yes, show the example pls. 2answers 2k views ### Proof Black Scholes Theta I saw the following proof of theta in a paper I read, and I thought it looked pretty neat. Unfortunately I don't understand the step that they do. This is what they do: Now, I don't get how they go ... 1answer 144 views ### Asian Call Option An Asian call option with the average strike payoff, uses the “averaging” to reduce the effect of volatility. Why is this so? 1answer 523 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^-... 1answer 50 views ### Why did Tiffany call's premium increase, when its stock price decreased? [closed] My grandma has been tracking TIF in the news, and recorded its option premiums. On Jun 9 2020, 1 TIF 2022-01-22 135C sold for \0.88. On Jun 10 2020, it sold for \0.5. Today, it sold for 1.6. Which ... 1answer 39 views ### Can the spread between option premium for bull call spread change over time? 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. ... 1answer 351 views ### option call question i have a question regarding a call option exercise i cant get my head around The price of a stock is 100, the continuously compounded risk free rate is 5%. The strike price of an european call option ... 2answers 251 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 ... 1answer 98 views ### Maximum value of a call option proof I'm reading Sinclair's Option Pricing and am confused by the proof for the maximum value of a call. It makes sense logically that a call can't be worth more than the underlying, and so: c <= S The ... 1answer 38 views ### Confused in regards to calculation of delta of one share including one call and one put [closed] Q:My investment portfolio has one share of one call and one put, what would be the delta of my portfolio ? delta of call:0.45 delta of put: -0.14 My thought process: To begin with since im dealing ... 1answer 119 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 ... 1answer 491 views ### Down-Out Call and Vanilla call price We all know from text books and practice that a knock out call is usually cheaper than a vanilla call option. Economically speaking, this comes from the fact that there is a probability bigger than ... 1answer 126 views ### Pricing of a call option in one period binomial model You are given a 5\% call option worth \2.66. The strike price k is \41.00. S(0)=40, Sd=35 (i.e the lower price of the stock at t=1) find Su (i.e the high price of the stock at t=1).... 0answers 43 views ### What can we say about digital puts and calls with different strike prices? I am a noob to the field of quantitative finance. I am reading this book by Mark S. Joshi. Can you help me make sense of one of the exercise questions? Here is the question (from page 40 of the book): ... 0answers 82 views ### Payoff of barrier options I was reading a research paper recently and the author defined payoffs of Up-and-Out and Down-and-Out barrier call options as max[0, ST - K]I(m < H) and max[0, ST - K]I(M > H) respectively. K is ... 0answers 23 views ### Modeling Basket Call Option If I had a market basket of three assets with payouts of: q being weights. There is a correlation between each pair of daily log-stock price shocks. How would you price this call option? How would ... 0answers 28 views ### 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 ... 0answers 36 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 0answers 71 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. ... 1answer 51 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 ... 0answers 224 views ### Higher Vega with ATM options when Spot is higher Which would have larger vega, an ATM call option at spot 100 or an ATM call option at spot 200. Apparently the answer is the one with ATM at spot 200. I am not sure how you get this answer. Why ... 0answers 81 views ### Different versions of Put-Call Parity Why is it stated sometimes that C - P = F and in wikipedia it statest that C - P = D(F-K), where D is the discount factor and K is the strike (of both the call and put?). Is this just affected ... 0answers 69 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 $v$ ...
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 $C^{2}_{0}$ ...