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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 $S2$ = ...
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I'm trying to derive an approximation for the zero-rebate barrier option under the Heston model: $$dS_t=\mu S_tdt+\sqrt{v_t}S_tdW^S_t$$ $$dv_t=\kappa(\bar{v}-v_t)dt+\eta\sqrt{v_t}dW^v_t,\quad d\langle ... 0answers 269 views Callable Bond = long Bond - call on bond? Can someone verify (maybe there is some literature around) the following relationships? Callable Bond= Long on Bond + short on a Call Position --> PV(CallableBond) = PV(Bond) - Call on Bond? or ... 1answer 81 views Derivation for call option upper bound In Euan Sinclair's book, Option Trading, he writes that c <= S, the price of a European call must be lower than the price of the underlying stock. To prove it, he applies the principle of no ... 0answers 90 views Heston Model Calibration with MatLab: model prices do not fall in the bid-ask range I am currently implementing the MatLab code reported below for the calibration of Heston Model. The code seems fine and, by reading the paper where I took the code, I was able to calibrate and price ... 0answers 38 views What is a call-spread and its formula? I am attempting Mark Joshi's The Concepts and Practice of Mathematical Finance. In B.3 Project 1: Vanilla options in a Black-Scholes world, he asked the following question. We need to be sure that ... 0answers 51 views Binomial Model - completeness in presence of arbitrage Consider a uniperiodal binomial model where I buy one bond of value B_0 and rate r=0.1, and h stocks with price S_0=5. The value of the portfolio at time t=0 is$$ V_0 = B_0 + hS_0, $$... 0answers 472 views Black Scholes Replicating Portfolio Riskfree Asset Im having a question about this standard derivation of the Black-Scholes formula: http://www.soarcorp.com/research/BS_hedging_portfolio.pdf The paper states$$C=\Delta S+B$$and finally \Delta = ... 0answers 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 41 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 77 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 21 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 35 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 15 views Is there a name and/or calculation to get the break-even for calls compared to holding plain stock? I recently found myself in the position of wanting to buy some leap calls instead of stock to get more leverage, I tried to calculate the pricepoint at which the leaps were returning more than just ... 0answers 67 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. ... 0answers 219 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 78 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 $v$ ...
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 ...