Henry Cobbe, CFA

Pleased to share our new research with Parviz Rakhmonov published in Review of Derivatives Research: "Stochastic volatility for factor Heath–Jarrow–Morton framework" We've extended the Factor Heath-Jarrow-Morton (FHJM) framework by incorporating stochastic volatility drivers that can capture the positive implied volatility skews observed in interest rate derivatives markets. Key contributions: • Analytical valuation formulas for swaptions and options on rate futures using moment generating functions • Implementation with both CIR and log-normal SV drivers • Application to Nelson-Siegel term structure model with successful calibration to USD swaptions and SOFR options • Novel convexity adjustment formulas that incorporate both skew and smile effects The framework provides a robust toolkit for pricing, risk management, and scenario generation for fixed income derivatives in an arbitrage-free manner. Full paper available (limited downloads): https://lnkd.in/dwEKvRn4 Working paper on SSRN: https://lnkd.in/dTBcrZBC Code implementation: https://lnkd.in/dUy54yxn #QuantitativeFinance #InterestRateModeling #StochasticVolatility #FixedIncome

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When 50% buy risky AT-1 bonds with incomplete info but only 13% with full disclosure, the game is rigged, finds Dvara Holdings. 57% of bank RMs admit bosses asked them to mis-sell unsuitable products, reveals 1Finance. Yet 85% don't even know the difference between regular and direct mutual funds. The tricks: RMs inserting their own contacts during verification, disguising mutual fund redemptions as "policy refunds," pitching discount cards as health insurance. AT-1 bonds wiped out Rs 8,400 crore. Banks got 7,576 mis-selling complaints last year. Your bank seller's paycheck depends on selling you the wrong product. Can you recognise when it happens? Yasmin Hussain tells the tale of these shocking tactics in this week's ET Wealth cover story. An ancient con that finds fresh prey every day. (P.S. Full story on The Economic Times website)

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The UK underlying growth picture is weaker than the headline GDP data suggests. I'm reading headlines like "Resilient Economy Supports Slower BOE Rate Cut Path" after this morning's UK GDP release. But how resilient is the economy really? Slide 1 shows the contribution to GDP growth from the key household consumption and business investment components of GDP. As you can see, these key measures of growth are slowing down. It's notable that business investment is contracting, as that is more volatile than consumption and the part of GDP which tends to lead the economy into recessions. Slide 2 shows that the boost to growth came mainly from government spending. While that's not to be ignored completely, it doesn't really tell you much about the underlying health of the economy. Slide 3 shows there was also a boost from inventories and a marginal boost from net trade. Inventories is a funny one because GDP accounting views an increase in inventories as a positive but what it really means is that the stock of unsold goods is rising. Retail's contribution to GDP, for example, contracted in Q2. Slide 4 shows that the HMRC PAYE data show public sector employment increasing, while private sector employment has been contracting for a whole year now. Slide 5 shows the breakdown of the decline in employment for some key private industries. Finally, slide 6 shows that while the business surveys had flagged a pick up in new orders in June (the month which was responsible for all of Q2's GDP growth) they are now pointing to a contraction again for July. So maybe best not to crack out the champagne just yet.

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Mean Reversion is Dead - Long Live Extreme Reversion What if the smart money is wrong about mean reversion? What if owning Credit today is not a leap of faith? What if 'mean reversion' is worse than extrapolation as a measure of expected returns today? What if the 'mean' is meaningless? A year ago, I posted a comic to illustrate that perspective was needed when thinking about spreads. IG Credit was around 90 basis points over Treasuries and well below the long-term mean of 129 bps. The 'path of least resistance is wider' commentary was starting to gather speed… Since then, spreads have tightened by 15 basis points. Credit has outpaced treasuries by 2.6% (excess return is 2%, of which, roughly half is carry and half is spread tightening). It bears repeating, selling Credit has been a losing trade. Spreads have tightened and you've given up carry versus Treasuries or Cash. And if you sold Credit solely because "spreads were tight" it's not analytically defensible. Firstly, Credit spreads are not normally distributed. As a statistic, the mean of a non-normal distribution has almost no information to impart about the relative level of spreads at any moment in time. Over the last 35 years: Mean  129 bps Mode   88 bps            Median 111 bps       Spreads are skewed heavily towards the left with an almost endless right tail of crisis driven spreads that peaked above 600 basis points To put this in perspective, 46% of monthly Credit spread observations are below 100 basis points. (Credit lived below 100 basis points for most of the 1990s - a seven-year run. We're barely two years into similar territory.) If any reversion is taking place, it is to the mode or, perhaps, the extreme. Secondly, even if the data was normally distributed, the entire data set loses significance if what is being measured is different at different points in time! It is quite possible that what began as a measurement of risk is now only a partial measurement of risk because the 'riskless' assets (Treasuries) are no longer so risk-free. I've argued this elsewhere, but the summary is stark: • Mega-cap Corporates are cash fortresses while the US drowns in debt • Post-2022, Credit volatility runs lower than Treasury volatility • Credit liquidity now rivals treasuries in ETFs and swaps  • AI productivity gains flow to corporations, not governments Vikas Jain recently plotted Credit spreads against both treasuries and swaps. The graph (see in comments) shows that Credit spreads to Treasuries and Credit spreads to swaps tracked closely until 2022, then split. The Treasury-Swap basis blew out, suggesting Treasuries now carry their own risk premium – something not captured in historical spreads. Without doubt, spreads will widen again. Risk cycles aren't dead - volatility might be the new normal. But I'd wager that over the long term, Credit spreads settle structurally lower versus Treasuries. The relationship has fundamentally changed. Position accordingly.

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There are interesting things happening in the Lithuanian bond market, and I wanted to explore some of them below. One of the attractive features of bond instruments is a fixed term, with a known maturity date, which allows you to predict the cashflows of your portfolio quite well, with a set coupon and bond repayment dates in mind. If the alternative financing is needed longer than expected, the usual way is to refinance this debt with a new bond issue, where the existing bondholders are asked to change their bonds into new ones being issued. An ongoing example of this is Urban HUB bonds currently being distributed, where existing bondholders can change their 10.75% coupon bonds into 8.5% yielding bonds. Nevertheless, we are observing in the market some examples of the extension of the bond term dates, where the maturity is brought forward to the future, due to the projects or bank financing not being finalized on time 🤓 A recent example of this is UAB “Metanira” bonds, which were issued to finance a residential development in Gandia, in the Valencia region of Spain, EUR 5.9 M in total. The bonds were initially issued with a 10% coupon rate with a maturity date commencing on the 5th of Sep 2025. At a recent bondholders’ meeting, the issuer offered to extend the maturity date to the 5th of March 2026 and to add a 2% premium to the last coupon payment. Another example is the ongoing saga of UAB “Orkela”, where the bonds were issued to finance st Jacobs’ commercial development in Vilnius. The programme was distributed in tranches, initially starting with 6% coupon and reaching 10% yield at the peak of EUR 38.66 M distribution programme, over the period of 2022 – 2024. In Jan 2025, the bondholders of Orkela were asked to vote to extend the terms of the bonds to July 2025, with the issuer offering 8% yield. In July 2025, the bondholders were subsequently asked to vote 2nd time to extend the issue to Oct 2025, with the issuer offering 9% yield. The 19th of October deadline is coming up, and it will be interesting to see whether the maturity date of these bonds will be further extended, the 3rd time. In my humble opinion – yes, as although the issuer is negotiating bank financing with the banks to refinance the bond debt, due to the nature of the largest tenants in the complex, which are a school and a hotel (which is yet to open), the banks might want to wait to see the revenue metrics of these tenants, and thus delay their financing decisions. This is not to say that these bonds will never be refinanced with traditional debt, only that it might take longer than expected due to the conservative profile of the banks. And if the outcome is, indeed, positive sooner, I think both the issuer and the bondholders will be happy and relieved, as the refinancing of large bond issues is never easy 🙏

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The days of hedge funds as a naive asset class are long behind us. Today, institutions with substantial allocations to hedge funds often have a very specific use case - that of portfolio diversification alongside (or in place of) traditional sources of portfolio ballast, such as core bonds. Underneath the headlines, those low-beta, diversifying strategies have been quietly doing their job, performing well. Check out our latest whitepaper below! Or visit the ACPM website to read more of our research. https://lnkd.in/gBiGkxt4

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