IFoA SP6 common mistakes
IFoA SP6 · Understand the traps and how to avoid them.
Pricing an option or swap with the wrong day-count or discounting convention, e.g. using simple interest over a multi-year horizon, or discounting with a continuously compounded rate when the question quotes an annual effective rate.
Candidates memorise the Black-Scholes formula and plug numbers in without checking that the quoted rate, tenor and compounding basis match the model's assumptions; SP6 questions deliberately mix conventions to test this.
What to do instead
Before computing, write down the rate basis, day-count and compounding frequency explicitly, then convert to the model's required convention (e.g. r_cc = ln(1+r_eff), or discount factor = 1/(1+r_eff)^t) in a labelled line. State the conversion in the answer so the marker can follow it.
Applying the Black-Scholes formula to an American-style option or to an asset paying a continuous dividend yield without adjusting for early exercise or the dividend term.
The formula is over-practised and candidates default to it; they miss cues in the question such as 'American', 'dividend yield q', or 'early exercise premium' and treat the problem as plain European vanilla.
What to do instead
Read the option description first and classify it: European/American, dividend-paying/non-paying, single/multi-asset. If American and dividends or carry make early exercise plausible, say so and use a binomial tree or note the early-exercise premium rather than quoting Black-Scholes. Include the e^{-qT} term in d1 and in the forward when a yield is given.
Confusing the greeks' definitions and signs, e.g. reporting vega as the change in option value per 1% change in volatility when the question asks per unit (1.00) change, or giving the wrong sign for theta on a long option.
Textbook formulas are often quoted per unit change, while market convention quotes vega per 1% vol move and theta per day; candidates copy a formula without reconciling units, and theta's negative sign for long options is easily dropped when rearranging.
What to do instead
Write the greek's unit next to it every time (e.g. 'vega = ∂V/∂σ per 1.00 vol point; per 1% divide by 100'). For theta, state the convention (per year or per day) and confirm the sign: a long option loses value as time passes, so theta is negative. Cross-check the magnitude against the option premium.
Building a binomial tree with the wrong up/down factors or risk-neutral probability, e.g. using u = e^{σ√Δt} with the wrong Δt, or p = (e^{rΔt} − d)/(u − d) with a dividend yield omitted.
The tree parameters depend on the time step, and candidates often use the total time to maturity instead of the step length, or forget that the risk-neutral drift must include the dividend yield or foreign rate.
What to do instead
Define Δt = T/N first, then u = e^{σ√Δt}, d = 1/u, and p = (e^{(r−q)Δt} − d)/(u − d). Check that p lies between 0 and 1 as a sanity test; if not, the step size or parameters are wrong. Verify the tree reprices a European option against Black-Scholes before using it for an American one.
Mixing up forward versus futures pricing, particularly ignoring the daily settlement/convexity adjustment or treating the futures price as identical to the forward price when rates are stochastic.
The cost-of-carry formula F = S e^{(r−q)T} is taught as the forward price, and the distinction between forwards and futures (convexity, margining) is a small syllabus point that candidates under-revise.
What to do instead
State explicitly whether the contract is a forward or a future. For futures, note that the futures price equals the forward price only when rates are deterministic; otherwise mention the convexity adjustment and its direction (futures price below forward when rates and asset prices are positively correlated). Show the carry calculation with the correct r and q.
Getting the put-call parity relationship wrong, especially for options on futures, options with dividends, or when the strike is discounted at the wrong rate.
Parity has several variants (C − P = S − Ke^{−rT}; C − P = (F − K)e^{−rT} for options on futures; with dividend yield C − P = Se^{−qT} − Ke^{−rT}) and candidates apply the spot version to a futures option or forget the discounting.
What to do instead
Derive parity from the replicating portfolio each time rather than recalling it: long call plus cash Ke^{−rT} equals long put plus the underlying. For options on futures the underlying is the forward, so C − P = (F − K)e^{−rT}. Use parity as a numerical check on any call and put you price.
Mis-specifying the payoff or profit diagram, e.g. omitting the premium, netting the wrong legs, or mislabelling breakeven points for spreads, straddles and collars.
Candidates draw the shape of the payoff correctly but forget that 'profit' includes the net premium paid or received, and complex multi-leg strategies have breakevens that are easy to compute incorrectly under time pressure.
What to do instead
Tabulate each leg separately: premium paid/received, strike, and payoff at expiry at key points (below lower strike, between strikes, above upper strike). Sum the legs to get net payoff, then subtract or add net premium for profit. Compute breakevens algebraically from the net payoff expression and check them on the sketch.
Using the wrong volatility in a pricing question, e.g. plugging in implied volatility when historical is given, or failing to convert an annual volatility to the correct horizon for a binomial step or a VaR calculation.
Questions often supply both historical and implied vol, and the correct choice depends on whether you are pricing to market or testing a model; also σ scales with √time, which candidates forget when shortening the horizon.
What to do instead
Identify the purpose: for marking to market use implied vol; for a model test or a risk estimate the question will specify. Scale volatility by √(horizon) explicitly (σ_Δt = σ√Δt) and state the units. If both vols are given, justify your choice in one sentence.
Ignoring credit risk and collateral in swap or derivative valuation, valuing a swap as risk-free when the counterparty is described as sub-investment grade or when a credit valuation adjustment is requested.
Standard swap valuation uses discount factors without credit adjustment, and candidates treat CVA as an optional extra rather than part of the required answer when the question mentions counterparty quality.
What to do instead
Check the question for counterparty credit quality, collateral terms and close-out conventions. If present, compute a CVA as the expected positive exposure times loss given default, discounted, and adjust the risk-free value. State the assumption (risk-free versus CVA-adjusted) whenever you value a swap.
Producing a numerical answer with no units, no sign convention and no interpretation, or failing to comment on whether the result is economically sensible (e.g. a negative probability, a negative forward price, an arbitrage profit left unexplained).
Candidates focus on getting the number and run out of time or confidence to write the concluding sentence; SP6 marks are awarded for interpretation and for spotting arbitrage or model limitations, not just arithmetic.
What to do instead
End every calculation with a one-line interpretation: state the unit (per share, per contract, in currency), the sign meaning (long/short, gain/loss) and a plausibility check. If the result implies arbitrage, say so and outline the replicating trade. Allocate the last minute of each question to this sentence.