In a one-period binomial model, write the up and down underlying values and the option's expectation form.

Underlying goes to $S_{0}u$ or $S_{0}d$. Option value: $$c = \frac{\pi c^{+} + (1-\pi) c^{-}}{1+r}$$ where $c^{+},c^{-}$ are up/down payoffs and $\pi$ is the risk-neutral up probability.

Give the risk-neutral probability of an up move in the binomial model.

$$\pi = \frac{(1+r) - d}{u - d}$$ where $u$ and $d$ are the up and down gross return factors and $r$ is the per-period risk-free rate.

What is risk-neutral valuation?

A pricing method where expected payoffs are computed using risk-neutral (not real-world) probabilities and discounted at the risk-free rate. It works because no-arbitrage pricing is independent of investors' risk preferences.

Define the hedge ratio (delta) in the one-period binomial model.

$$h = \frac{c^{+} - c^{-}}{S_{0}u - S_{0}d}$$ the number of units of the underlying needed per option to form a risk-free hedged portfolio.

How does a multi-period binomial model extend the one-period model?

It builds a recombining tree of underlying prices over many steps; option value is found by computing terminal payoffs and folding back through the tree using risk-neutral probabilities, discounting one period at a time (allowing early-exercise checks for American options).

State the Black-Scholes-Merton formula for a European call (no dividends).

$$c = S_{0}N(d_{1}) - X e^{-rT} N(d_{2})$$ with $$d_{1}=\frac{\ln(S_{0}/X)+(r+\tfrac{1}{2}\sigma^{2})T}{\sigma\sqrt{T}},\quad d_{2}=d_{1}-\sigma\sqrt{T}.$$

List the key assumptions of the Black-Scholes-Merton model.

Underlying follows geometric Brownian motion with constant volatility; continuous trading with no transaction costs or taxes; constant known risk-free rate; no arbitrage; lognormally distributed prices; European-style exercise; (basic form) no dividends.

Define the option Greek delta and its sign for calls and puts.

Delta is the sensitivity of option price to the underlying: $\Delta = \frac{\partial c}{\partial S}$. Call delta ranges $0$ to $1$ ($N(d_1)$); put delta ranges $-1$ to $0$.

Gamma measures the rate of change of delta with respect to the underlying price: $\Gamma = \frac{\partial^{2} c}{\partial S^{2}}$. It is largest for at-the-money options near expiration and is positive for long options.

Define vega and its relationship to volatility.

Vega is the sensitivity of the option price to a change in the underlying's volatility: $\text{vega} = \frac{\partial c}{\partial \sigma}$. Both long calls and long puts have positive vega.

🇮🇳 CFA (Chartered Financial Analyst) · flashcards

CFA (Chartered Financial Analyst) Derivatives and Alternative Investments Flashcards

50 question-and-answer cards covering Derivatives and Alternative Investments as it is examined in CFA (Chartered Financial Analyst). 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.

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In a one-period binomial model, write the up and down underlying values and the option's expectation form.
Underlying goes to $S_{0}u$ or $S_{0}d$. Option value: $$c = \frac{\pi c^{+} + (1-\pi) c^{-}}{1+r}$$ where $c^{+},c^{-}$ are up/down payoffs and $\pi$ is the risk-neutral up probability.
Give the risk-neutral probability of an up move in the binomial model.
$$\pi = \frac{(1+r) - d}{u - d}$$ where $u$ and $d$ are the up and down gross return factors and $r$ is the per-period risk-free rate.
What is risk-neutral valuation?
A pricing method where expected payoffs are computed using risk-neutral (not real-world) probabilities and discounted at the risk-free rate. It works because no-arbitrage pricing is independent of investors' risk preferences.
Define the hedge ratio (delta) in the one-period binomial model.
$$h = \frac{c^{+} - c^{-}}{S_{0}u - S_{0}d}$$ the number of units of the underlying needed per option to form a risk-free hedged portfolio.
How does a multi-period binomial model extend the one-period model?
It builds a recombining tree of underlying prices over many steps; option value is found by computing terminal payoffs and folding back through the tree using risk-neutral probabilities, discounting one period at a time (allowing early-exercise checks for American options).
State the Black-Scholes-Merton formula for a European call (no dividends).
$$c = S_{0}N(d_{1}) - X e^{-rT} N(d_{2})$$ with $$d_{1}=\frac{\ln(S_{0}/X)+(r+\tfrac{1}{2}\sigma^{2})T}{\sigma\sqrt{T}},\quad d_{2}=d_{1}-\sigma\sqrt{T}.$$
List the key assumptions of the Black-Scholes-Merton model.
Underlying follows geometric Brownian motion with constant volatility; continuous trading with no transaction costs or taxes; constant known risk-free rate; no arbitrage; lognormally distributed prices; European-style exercise; (basic form) no dividends.
Define the option Greek delta and its sign for calls and puts.
Delta is the sensitivity of option price to the underlying: $\Delta = \frac{\partial c}{\partial S}$. Call delta ranges $0$ to $1$ ($N(d_1)$); put delta ranges $-1$ to $0$.
Define gamma.
Gamma measures the rate of change of delta with respect to the underlying price: $\Gamma = \frac{\partial^{2} c}{\partial S^{2}}$. It is largest for at-the-money options near expiration and is positive for long options.
Define vega and its relationship to volatility.
Vega is the sensitivity of the option price to a change in the underlying's volatility: $\text{vega} = \frac{\partial c}{\partial \sigma}$. Both long calls and long puts have positive vega.
Define theta.
Theta measures the change in option value as time passes (time decay): $\Theta = \frac{\partial c}{\partial t}$. It is generally negative for long options, which lose time value as expiration approaches.
Define rho.
Rho is the sensitivity of the option price to the risk-free interest rate: $\rho = \frac{\partial c}{\partial r}$. Calls have positive rho; puts have negative rho.
How does dynamic delta hedging work?
A position is made delta-neutral by offsetting option delta with the underlying; because delta changes (gamma), the hedge must be rebalanced continuously. In BSM, continuous rebalancing replicates the option exactly, the basis of no-arbitrage pricing.
Describe a covered call and its payoff profile.
Long the underlying plus short a call. It generates premium income and caps upside above the strike while leaving downside exposure (reduced by the premium). Used to monetize a neutral-to-mildly-bullish view.
Describe a protective put.
Long the underlying plus long a put. It insures against downside below the strike (loss floored at strike minus premium) while retaining full upside minus the premium cost — like buying insurance.
Describe a bull call spread and when it is used.
Buy a lower-strike call and sell a higher-strike call (same expiry). It lowers net cost and caps both gain and loss; used for a moderately bullish view. Max profit is the strike difference minus net premium.
Describe a straddle and the view it expresses.
Buy a call and a put at the same strike and expiry. It profits from large moves in either direction (high volatility view); maximum loss is the combined premiums if the underlying stays near the strike.
Define alternative investments and their general characteristics versus traditional assets.
Alternatives include private equity, private debt, real estate, infrastructure, hedge funds, and natural resources/commodities. They typically feature illiquidity, less regulation/transparency, higher fees, limited historical data, potential diversification, and specialized management.
Describe the typical hedge fund fee structure ('2 and 20') and key provisions.
Roughly a 2% management fee on assets plus a 20% incentive/performance fee on profits. Common provisions: a hurdle rate (minimum return before incentive fees) and a high-water mark (incentive fees only on new cumulative gains).
What is the difference between a hard hurdle rate and a soft hurdle rate?
With a hard hurdle, incentive fees apply only to returns above the hurdle. With a soft hurdle, once the hurdle is met, the incentive fee is charged on the entire return (not just the excess).
Distinguish private equity, venture capital, and leveraged buyouts.
Private equity invests in non-public companies. Venture capital funds early-stage/growth firms. Leveraged buyouts acquire mature companies using substantial debt, aiming to improve operations and exit at a profit. Private debt lends directly (e.g., direct lending, mezzanine, distressed).
Compare the four main real estate investment approaches across public/private and debt/equity.
Private equity: direct property ownership. Private debt: mortgages/loans. Public equity: REITs/REOCs. Public debt: mortgage-backed securities (MBS). They differ in liquidity, leverage, and return drivers.
Why is infrastructure considered an alternative asset, and what are its typical features?
Infrastructure (roads, utilities, airports) offers long-lived, capital-intensive assets with stable, often inflation-linked cash flows and low correlation to other assets. Brownfield (existing) assets carry less risk; greenfield (new build) carries development risk.
Why are standard mean-variance metrics often misleading for alternative investments, and what risk issues arise?
Returns are often smoothed/appraisal-based and illiquid, biasing reported volatility and correlations downward and inflating Sharpe ratios. Returns are non-normal (negative skew, fat tails), so survivorship/backfill bias, leverage, and tail risk must be considered, favoring downside measures like VaR or Sortino.

What this deck covers

The Derivatives and Alternative Investments deck follows the CFA (Chartered Financial Analyst) Derivatives and Alternative Investments syllabus — 3 chapters and 12 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 16.7 cards per chapter.

Answers are written to be recallable, not just readable — averaging about 215 characters, which is long enough to carry the reasoning and short enough to say out loud.

A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.

Derivatives and Alternative Investments flashcards FAQ

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50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.

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They follow the CFA (Chartered Financial Analyst) Derivatives and Alternative Investments syllabus — 3 chapters and 12 topics — so the questions track what is actually examinable.

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Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.