FINC306 LATEST 2026 TESTS PAPER QUESTIONS AND
ANSWERS GUARANTEE A+
✔✔What is implied volatility? - ✔✔The volatility required to get the price when other
variables are fixed.
✔✔What is a method of finding the implied volatility? How is this convertable into a
minimisation problem? - ✔✔- f(vol.)= c(St,r,delta,vol implied, tau, K)-c
- (c(St,r,delta,vol implied, tau, K)-c)^2
✔✔What is the Newton Rapson Method and how is it applied to find implied volatility? -
✔✔x_n+1 = x_n - f(xn)/f'(xn)
So = vol implied - (call formula)/(Vega: dc/dsigma)
✔✔What are 4 methods of approximating black scholes? - ✔✔- Binomial Tree
- Monte Carlo Simulation
- Mathematically (Taylor Series)
- Finite difference
✔✔What are the steps of monte carlo simulation? - ✔✔- Pick a number from a uniform
distribution
- Apply a normal inverse distribution to obtain X
- We can find X via formula for ST
- Calculate c value as max (ST-K,0)
- Repeat N times
- Calculate expected value and discount
✔✔What is the primary reason Monte Carlo simulation is considered overkill for
standard European options? - ✔✔Because simpler methods (like Black-Scholes or
Binomial Trees) provide closed-form or fast numerical solutions.
✔✔Monte Carlo simulations approximate the Black-Scholes formula by generating a
large number of future stock prices based on what type of probability distribution? -
✔✔A continuous distribution, specifically the Normal density.
✔✔In the context of option pricing, Monte Carlo simulation relies on the principle of the
Risk-Neutral Valuation formula. What rate is used to discount the expected future payoff
to get the current price? - ✔✔The risk-free rate.
✔✔For which class of options is the full simulation of the stock price path (intermediate
steps between t and T) typically necessary when using Monte Carlo methods? -
✔✔Path-dependent exotic options (e.g., Asian options where payoff depends on the
average price over time).
, ✔✔The method of mathematical approximation is typically used to simplify the Black-
Scholes formula by using the Taylor (or Maclaurin) series to approximate which
function? - ✔✔The Standard Normal Cumulative Distribution Function (N(x)).
✔✔Why is mathematical approximation needed when using older computational tools
(like allowed scientific calculators)? - ✔✔Because these tools cannot easily calculate
values of the standard normal cumulative distribution function (N(x)) required for the
Black-Scholes formula.
✔✔The Finite Difference Method converts the Black-Scholes model from an analytic
solution into a numerical problem by substituting the partial derivatives with
approximations from what principle? - ✔✔Finite differences.
✔✔What fundamental equation of option pricing serves as the starting point for applying
the Finite Difference Method? - ✔✔The Black-Scholes Partial Differential Equation
(PDE).
✔✔In the Explicit Finite Difference method, how does the numerical calculation of the
option price proceed through time? - ✔✔It works backward in time from maturity (T) to
earlier times (t−Δt).
✔✔Which Finite Difference method requires solving a system of equations because the
option value at time t+Δt depends on values at time t? - ✔✔The Implicit Finite Difference
method.
✔✔Which type of Finite Difference method combines aspects of both the Explicit and
Implicit methods, leading to improved stability and accuracy? - ✔✔The Crank-Nicolson
method.
✔✔In FDM, when solving for an American call option, what boundary condition is set at
S = 0 (zero stock price)? - ✔✔Zero (V = 0).
✔✔When applying FDM, the price of the option at time T (maturity) is the τ-direction
initial condition. How is it determined? - ✔✔From the payoff function (e.g., c(T) =
max(S(T) − K, 0) for a call).
✔✔What is Ad-hoc Black Scholes and whats equation? Whats the key problem with
original equation it solves? - ✔✔- BS standard assumes constant volatility for all strikes
and maturities
- Ad Hoc Black Scholes relaxes the constant volatility assumption
- Volatility = B0+B1K+B2T+B3K^2+B4T^2+B5KT
- Varies by number of polynomials, expressions for moneyness and tau
ANSWERS GUARANTEE A+
✔✔What is implied volatility? - ✔✔The volatility required to get the price when other
variables are fixed.
✔✔What is a method of finding the implied volatility? How is this convertable into a
minimisation problem? - ✔✔- f(vol.)= c(St,r,delta,vol implied, tau, K)-c
- (c(St,r,delta,vol implied, tau, K)-c)^2
✔✔What is the Newton Rapson Method and how is it applied to find implied volatility? -
✔✔x_n+1 = x_n - f(xn)/f'(xn)
So = vol implied - (call formula)/(Vega: dc/dsigma)
✔✔What are 4 methods of approximating black scholes? - ✔✔- Binomial Tree
- Monte Carlo Simulation
- Mathematically (Taylor Series)
- Finite difference
✔✔What are the steps of monte carlo simulation? - ✔✔- Pick a number from a uniform
distribution
- Apply a normal inverse distribution to obtain X
- We can find X via formula for ST
- Calculate c value as max (ST-K,0)
- Repeat N times
- Calculate expected value and discount
✔✔What is the primary reason Monte Carlo simulation is considered overkill for
standard European options? - ✔✔Because simpler methods (like Black-Scholes or
Binomial Trees) provide closed-form or fast numerical solutions.
✔✔Monte Carlo simulations approximate the Black-Scholes formula by generating a
large number of future stock prices based on what type of probability distribution? -
✔✔A continuous distribution, specifically the Normal density.
✔✔In the context of option pricing, Monte Carlo simulation relies on the principle of the
Risk-Neutral Valuation formula. What rate is used to discount the expected future payoff
to get the current price? - ✔✔The risk-free rate.
✔✔For which class of options is the full simulation of the stock price path (intermediate
steps between t and T) typically necessary when using Monte Carlo methods? -
✔✔Path-dependent exotic options (e.g., Asian options where payoff depends on the
average price over time).
, ✔✔The method of mathematical approximation is typically used to simplify the Black-
Scholes formula by using the Taylor (or Maclaurin) series to approximate which
function? - ✔✔The Standard Normal Cumulative Distribution Function (N(x)).
✔✔Why is mathematical approximation needed when using older computational tools
(like allowed scientific calculators)? - ✔✔Because these tools cannot easily calculate
values of the standard normal cumulative distribution function (N(x)) required for the
Black-Scholes formula.
✔✔The Finite Difference Method converts the Black-Scholes model from an analytic
solution into a numerical problem by substituting the partial derivatives with
approximations from what principle? - ✔✔Finite differences.
✔✔What fundamental equation of option pricing serves as the starting point for applying
the Finite Difference Method? - ✔✔The Black-Scholes Partial Differential Equation
(PDE).
✔✔In the Explicit Finite Difference method, how does the numerical calculation of the
option price proceed through time? - ✔✔It works backward in time from maturity (T) to
earlier times (t−Δt).
✔✔Which Finite Difference method requires solving a system of equations because the
option value at time t+Δt depends on values at time t? - ✔✔The Implicit Finite Difference
method.
✔✔Which type of Finite Difference method combines aspects of both the Explicit and
Implicit methods, leading to improved stability and accuracy? - ✔✔The Crank-Nicolson
method.
✔✔In FDM, when solving for an American call option, what boundary condition is set at
S = 0 (zero stock price)? - ✔✔Zero (V = 0).
✔✔When applying FDM, the price of the option at time T (maturity) is the τ-direction
initial condition. How is it determined? - ✔✔From the payoff function (e.g., c(T) =
max(S(T) − K, 0) for a call).
✔✔What is Ad-hoc Black Scholes and whats equation? Whats the key problem with
original equation it solves? - ✔✔- BS standard assumes constant volatility for all strikes
and maturities
- Ad Hoc Black Scholes relaxes the constant volatility assumption
- Volatility = B0+B1K+B2T+B3K^2+B4T^2+B5KT
- Varies by number of polynomials, expressions for moneyness and tau
