Questions tagged [call]
The call tag has no usage guidance.
25
questions with no upvoted or accepted answers
5
votes
0
answers
1k
views
Greeks of a Basket Option
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
$S2$ = ...
- 51
4
votes
0
answers
186
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:
$$dS_t=\mu S_tdt+\sqrt{v_t}S_tdW^S_t$$
$$dv_t=\kappa(\bar{v}-v_t)dt+\eta\sqrt{v_t}dW^v_t,\quad d\langle ...
- 1,012
2
votes
0
answers
99
views
Path integral approach to price call option on zero coupon bonds
I am given the following identities:
$$
Z[J,t_1,t_2]=\int D W e^{\int_{t_1}^{t_2}dtJ(t)W(t)}e^{S}=e^{\frac{1}{2}\int_{t_1}^{t_2}dtJ(t)^2}
$$
$$
\int_t^Tdx\alpha(t,x)=\frac{1}{2}\left[\int_t^Tdx\sigma(...
- 133
2
votes
0
answers
337
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 ...
- 209
1
vote
0
answers
119
views
Heston model characteristic function
The characteristic function of $x=ln(S_T)$ in the framework of Heston model is guessed to be: $$f_j(\phi,x,v)=e^{C_j(\tau,\phi)+D_j(\tau,\phi)+i\phi x}$$
The call price is guessed to have the form: $$...
- 21
1
vote
0
answers
257
views
Call probability of a callable swap
For one call date,
The call probability is just the probability that the swap rate for the remaining life of the swap is below the strike rate. This is easily obtainable in a normal vol model, it is :
...
- 11
1
vote
0
answers
107
views
local volatility not reasonable
We are going to generate synthetic option prices using a Heston model, i.e.,
$$
\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*}
$$
...
- 11
1
vote
0
answers
144
views
Replicating call option in market which only trades stock and forward contracts
I am having a bit of trouble with a problem I've been given.
Consider a market which only trades a stock and forward contracts. There's only time 0 and 1.
Initial stock price S_0 is 10, the forward ...
- 11
1
vote
0
answers
514
views
Heston Model Calibration with MatLab: model prices do not fall in the bid-ask range
I am currently implementing the MatLab code reported below for the calibration of Heston Model. The code seems fine and, by reading the paper where I took the code, I was able to calibrate and price ...
1
vote
0
answers
104
views
What is a call-spread and its formula?
I am attempting Mark Joshi's The Concepts and Practice of Mathematical Finance.
In B.3 Project 1: Vanilla options in a Black-Scholes world, he asked the following question.
We need to be sure that ...
- 840
1
vote
0
answers
76
views
Binomial Model - completeness in presence of arbitrage
Consider a uniperiodal binomial model where I buy one bond of value $B_0$ and rate $r=0.1$, and $h$ stocks with price $S_0=5$. The value of the portfolio at time $t=0$ is
$$ V_0 = B_0 + hS_0, $$
...
- 111
1
vote
0
answers
601
views
Black Scholes Replicating Portfolio Riskfree Asset
Im having a question about this standard derivation of the Black-Scholes formula:
http://www.soarcorp.com/research/BS_hedging_portfolio.pdf
The paper states
$$C=\Delta S+B$$
and finally $\Delta = ...
- 5,795
1
vote
0
answers
86
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}{\...
- 77
0
votes
1
answer
46
views
Obtain B-S-M from a binomial tree as n goes to infinty using Lebesgue integral
My question is simple, consider a European call with payoff max(S_T-K, 0), Let's suppose that the underlying stock follows a binomial tree with up and down factors I know as we take n goes to infinity ...
- 1
0
votes
0
answers
75
views
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) ...
- 45
0
votes
0
answers
81
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):
...
- 153
0
votes
0
answers
164
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 ...
- 23
0
votes
0
answers
43
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 ...
- 2,045
0
votes
0
answers
49
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
- 1
0
votes
0
answers
115
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. ...
- 107
0
votes
0
answers
340
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 ...
- 2,492
0
votes
0
answers
152
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 ...
- 2,492
0
votes
0
answers
76
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 $v$ ...
- 1,243
-1
votes
1
answer
263
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 ...
-2
votes
1
answer
94
views
Pricing a European call option that has one underlying asset to compare with strike but 2 underlyings as payout
This is a real world problem and not a research one.
We are being proposed to buy an option that has to be exercised on a specific date T. So it is a European option.
This option has a strike price of ...
- 1