Global stocks held their nerve on Tuesday, as investors on either side of the Atlantic reacted with differing degrees of confidence that a peace deal will be agreed between the US and Iran to reopen the Strait of Hormuz. Closer to home, shares dipped slightly during an otherwise light trading day.DUBLINThe Iseq All-Share index fell by 0.32 per cent on Tuesday to close the trading day at 14,233.55, following another light volume session of trading in Ireland.The banking sector saw mixed results, with AIB’s share price falling by 0.92 per cent to close at €10.76 and PTSB remaining steady on €2.95. Bank of Ireland fared better than its rivals, edging up 0.24 per cent, to end the day at €18.97.Housebuilder Glenveagh Properties saw its share price rise by 1.62 per cent to close at €2.51, while insulation and building material specialists Kingspan Group was up 1.99 per cent on €97.15 in advance of a €900 million deal that was announced after markets closed. Stock in wind and solar energy group Greencoat Renewables was up 2.35 per cent, the largest percentage rise of any index constituent.Glanbia saw its share price fall back 2.41 per cent to close the day at €23.44, while stock in Ryanair also slid, by 0.88 per cent to €24.68.LONDONThe London Stock Exchange remained largely steady throughout the day. While the blue-chip FTSE 100 index fell by 0.17 per cent, it was somewhat offset by the mid-cap FTSE 250 gaining by 0.22 per cent at close of business.In a similar day to its Irish neighbours, the UK banking sector saw prices come under pressure. Shares in Lloyds Banking Group on the FTSE 100 fell by 0.74 per cent by close, while NatWest dropped by 0.34 per cent. Oil and gas giant BP saw much more positive returns, with its shares adding 2.15 per cent despite concerns growing that a peace-deal between the US and Iran, which could reopen the Strait of Hormuz, is looking less likely. Vodafone Group rebounded by 1.28, having fallen by 3.07 per cent the previous trading day. On the more domestically-focused FTSE 250, shoe makers Doc Marten’s share price rose by 3.34 per cent.EUROPEElsewhere in Europe, stocks remained steady around the record highs they have hovered close to in recent trading days. The pan-European Stoxx 600 rose fractionally, by 0.01 per cent, as investors balanced economic optimism closer to home with geopolitical risks further afield.With Bloomberg News reporting comments from Pakistan’s defence minister that the US and Iran are nearing “some sort of agreement”, oil prices broadly increased by 1.2 per cent on Tuesday. The energy sector jumped 1.7 per cent, while tech shares rose 1.1 per cent, providing further support. That sector remains among Europe’s top performers this year, up about 24 per cent year to date.Danish facility manager, ISS gained 4.4 per cent after reporting half-year results above estimates. Spirax Group slid 5.6 per cent to the bottom of the Stoxx 600 after the engineering firm ​reiterated its full-year forecast for mid-single-digit organic revenue growth and margin expansion.NEW YORKEarly trading of stocks on Wall Street indicated that US investors were matching the caution of their European counterparts, largely avoiding heavy bets on the market. Both the Dow Jones Industrial Average and the S&P 500 fell slightly by 1pm New York time, by 0.16 per cent and 0.18 per cent respectively. The strongest stocks on the S&P during early trade appeared to be investment firm KKR, rising by around 6 per cent, and Axon Enterprise, also around 6 per cent. Engineering firm Amentum Holdings was in the red from early, with its share price falling some 6 per cent.Household brand names Apple, Nike and Amazon were off to rocky starts on the Dow Jones Industrial Average Tuesday morning, with the tech giant falling some half a per cent, the sports brand by around 2.6 per cent and the online retail giant by 2.3 per cent. – Additional reporting: Reuters, Bloomberg